# Submit Info #55188

Problem Lang User Status Time Memory
Partition Function java sounansya AC 3794 ms 113.16 MiB

ケース詳細
Name Status Time Memory
0_00 AC 54 ms 9.20 MiB
100000_00 AC 988 ms 54.27 MiB
10000_00 AC 213 ms 15.53 MiB
1000_00 AC 79 ms 10.17 MiB
100_00 AC 53 ms 9.33 MiB
1_00 AC 51 ms 9.20 MiB
200000_00 AC 1938 ms 88.63 MiB
300000_00 AC 3773 ms 102.86 MiB
400000_00 AC 3791 ms 113.16 MiB
500000_00 AC 3794 ms 107.77 MiB
example_00 AC 53 ms 9.22 MiB

import java.util.*; import java.io.*; class Main { private static void solve() { int n = sc.nextInt() + 1; var p = new long[n]; int u = 0; int k = 1; for (; u * (3 * u - 1) / 2 < n;) { if (k % 4 < 2) p[u * (3 * u - 1) / 2] = 1; else p[u * (3 * u - 1) / 2] = -1; k++; if (u <= 0) u = -u + 1; else u = -u; } final int mod = 998244353; long[] f = { mp(p[0], mod - 2, mod) }; for (int i = 0; i < n; i++) if (p[i] != 0) p[i] = mod - p[i]; for (int i = 1, mm = n << 1; i < mm; i <<= 1) { var f2 = Arrays.copyOf(Convolution.convolution(f, f), Math.min(n, i << 1)); var f2p = Arrays.copyOf(Convolution.convolution(f2, Arrays.copyOf(p, i)), Math.min(n, i << 1)); for (int j = 0; j < f.length; j++) { f2p[j] += f[j] << 1; if (f2p[j] >= mod) f2p[j] -= mod; if (f2p[j] >= mod) f2p[j] -= mod; } f = f2p; } ou.printArray(Arrays.copyOf(f, n)); } private static long mp(long a, long b, long m) { if (b == 0) return 1; if ((b & 1) == 1) return (a * mp(a, b - 1, m)) % m; return mp((a * a) % m, b >> 1, m); } public static void main(String[] args) { solve(); ou.flush(); ou.close(); } private static ContestScanner sc = new ContestScanner(); private static ContestPrinter ou = new ContestPrinter(); } class Convolution { private final static int mod = 998244353; private final static int primitiveRoot = 3; private static long pow(long x, long n, int m) { if (m == 1) return 0; long r = 1; long y = x % m; while (n > 0) { if ((n & 1) != 0) r = (r * y) % m; y = (y * y) % m; n >>= 1; } return r; } private static int ceilPow2(int n) { int x = 0; while ((1L << x) < n) x++; return x; } private static long[] sumE(int mod, int g) { long[] sum_e = new long[30]; long[] es = new long[30]; long[] ies = new long[30]; int cnt2 = Integer.numberOfTrailingZeros(mod - 1); long e = pow(g, (mod - 1) >> cnt2, mod); long ie = pow(e, mod - 2, mod); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e = e * e % mod; ie = ie * ie % mod; } long now = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_e[i] = es[i] * now % mod; now = now * ies[i] % mod; } return sum_e; } private static long[] sumIE(int mod, int g) { long[] sum_ie = new long[30]; long[] es = new long[30]; long[] ies = new long[30]; int cnt2 = Integer.numberOfTrailingZeros(mod - 1); long e = pow(g, (mod - 1) >> cnt2, mod); long ie = pow(e, mod - 2, mod); for (int i = cnt2; i >= 2; i--) { es[i - 2] = e; ies[i - 2] = ie; e = e * e % mod; ie = ie * ie % mod; } long now = 1; for (int i = 0; i < cnt2 - 2; i++) { sum_ie[i] = ies[i] * now % mod; now = now * es[i] % mod; } return sum_ie; } private static void butterflyInv(long[] a, long[] sumIE, int mod) { int n = a.length; int h = ceilPow2(n); for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); long inow = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { long l = a[i + offset]; long r = a[i + offset + p]; a[i + offset] = (l + r) % mod; a[i + offset + p] = (mod + l - r) * inow % mod; } int x = Integer.numberOfTrailingZeros(~s); inow = inow * sumIE[x] % mod; } } } private static void butterfly(long[] a, long[] sumE, int mod) { int n = a.length; int h = ceilPow2(n); for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); long now = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { long l = a[i + offset]; long r = a[i + offset + p] * now % mod; a[i + offset] = (l + r) % mod; a[i + offset + p] = (l - r + mod) % mod; } int x = Integer.numberOfTrailingZeros(~s); now = now * sumE[x] % mod; } } } public static long[] convolution(long[] a, long[] b) { int n = a.length; int m = b.length; if (n == 0 || m == 0) return new long[0]; int z = 1 << ceilPow2(n + m - 1); { long[] na = new long[z]; long[] nb = new long[z]; System.arraycopy(a, 0, na, 0, n); System.arraycopy(b, 0, nb, 0, m); a = na; b = nb; } int g = primitiveRoot; long[] sume = sumE(mod, g); long[] sumie = sumIE(mod, g); butterfly(a, sume, mod); butterfly(b, sume, mod); for (int i = 0; i < z; i++) a[i] = a[i] * b[i] % mod; butterflyInv(a, sumie, mod); a = java.util.Arrays.copyOf(a, n + m - 1); long iz = pow(z, mod - 2, mod); for (int i = 0; i < n + m - 1; i++) a[i] = a[i] * iz % mod; return a; } } class ContestScanner { private final InputStream in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; public ContestScanner(InputStream in) { this.in = in; } public ContestScanner() { this(System.in); } private boolean hasNextByte() { if (ptr < buflen) return true; ptr = 0; try { buflen = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } return buflen > 0; } private int readByte() { return hasNextByte() ? buffer[ptr++] : -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } public boolean hasNext() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } public void nextThrow(int n) { for (int i = 0; i < n; i++) this.next(); } public void nextThrow() { this.nextThrow(1); } public long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) throw new NumberFormatException(); while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) return minus ? -n : n; else throw new NumberFormatException(); b = readByte(); } } public int nextInt() { long nl = nextLong(); if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException(); return (int) nl; } public double nextDouble() { return Double.parseDouble(next()); } public boolean[] nextBoolean(char True) { String s = this.next(); int n = s.length(); boolean[] array = new boolean[n]; for (int i = 0; i < n; i++) array[i] = s.charAt(i) == True; return array; } public long[] nextLongArray(int length) { long[] array = new long[length]; for (int i = 0; i < length; i++) array[i] = this.nextLong(); return array; } public long[] nextLongArray(int length, java.util.function.LongUnaryOperator map) { long[] array = new long[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsLong(this.nextLong()); return array; } public long[] nextLongArray(int length, long[] a) { long[] array = new long[length + a.length]; for (int i = 0; i < length; i++) array[i] = this.nextLong(); for (int i = length; i < array.length; i++) array[i] = a[i - length]; return array; } public int[] nextIntArray(int length) { int[] array = new int[length]; for (int i = 0; i < length; i++) array[i] = this.nextInt(); return array; } public int[] nextIntArray(int length, java.util.function.IntUnaryOperator map) { int[] array = new int[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsInt(this.nextInt()); return array; } public int[] nextIntArray(int length, int[] array) { int n = length + array.length; int[] a = new int[n]; for (int i = 0; i < length; i++) a[i] = this.nextInt(); for (int i = length; i < n; i++) a[i] = array[i - length]; return a; } public Integer[] nextIntegerArray(int length, java.util.function.IntUnaryOperator map) { Integer[] array = new Integer[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsInt(this.nextInt()); return array; } public Integer[] nextIntegerArray(int length) { Integer[] array = new Integer[length]; for (int i = 0; i < length; i++) array[i] = this.nextInt(); return array; } public double[] nextDoubleArray(int length) { double[] array = new double[length]; for (int i = 0; i < length; i++) array[i] = this.nextDouble(); return array; } public double[] nextDoubleArray(int length, java.util.function.DoubleUnaryOperator map) { double[] array = new double[length]; for (int i = 0; i < length; i++) array[i] = map.applyAsDouble(this.nextDouble()); return array; } public String[] nextArray(int length) { String[] array = new String[length]; for (int i = 0; i < length; i++) array[i] = this.next(); return array; } public long[][] nextLongMatrix(int height, int width) { long[][] mat = new long[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = this.nextLong(); return mat; } public int[][] nextIntMatrix(int height, int width) { int[][] mat = new int[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = this.nextInt(); return mat; } public int[][] nextIntMatrix(int height, int width, java.util.function.IntUnaryOperator map) { int[][] mat = new int[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = map.applyAsInt(this.nextInt()); return mat; } public double[][] nextDoubleMatrix(int height, int width) { double[][] mat = new double[height][width]; for (int h = 0; h < height; h++) for (int w = 0; w < width; w++) mat[h][w] = this.nextDouble(); return mat; } public boolean[][] nextBooleanMatrix(int height, int width, char True) { boolean[][] mat = new boolean[height][width]; for (int h = 0; h < height; h++) { String s = this.next(); for (int w = 0; w < width; w++) mat[h][w] = s.charAt(w) == True; } return mat; } public char[][] nextCharMatrix(int height, int width) { char[][] mat = new char[height][width]; for (int h = 0; h < height; h++) { String s = this.next(); for (int w = 0; w < width; w++) mat[h][w] = s.charAt(w); } return mat; } public char[][] nextCharMatrix(int height, int width, int h, int w, char c) { char[][] mat = new char[height + 2 * h][width + 2 * w]; for (int i = 0; i < height; i++) { String s = this.next(); for (int j = 0; j < width; j++) mat[i + h][j + w] = s.charAt(j); } for (int i = 0; i < h; i++) for (int j = 0; j < 2 * w + width; j++) mat[i][j] = c; for (int i = h + height; i < 2 * h + height; i++) for (int j = 0; j < 2 * w + width; j++) mat[i][j] = c; for (int i = h; i < h + height; i++) { for (int j = 0; j < w; j++) mat[i][j] = c; for (int j = w + width; j < 2 * w + width; j++) mat[i][j] = c; } return mat; } public boolean[][] nextBooleanMatrix(int height, int width, int h, int w, char c) { boolean[][] mat = new boolean[height + 2 * h][width + 2 * w]; for (int i = 0; i < height; i++) { String s = this.next(); for (int j = 0; j < width; j++) mat[i + h][j + w] = s.charAt(j) == c; } return mat; } } class ContestPrinter extends PrintWriter { public ContestPrinter(PrintStream stream) { super(stream); } public ContestPrinter() { super(System.out); } private static String dtos(double x, int n) { StringBuilder sb = new StringBuilder(); if (x < 0) { sb.append('-'); x = -x; } x += Math.pow(10, -n) / 2; sb.append((long) x); sb.append("."); x -= (long) x; for (int i = 0; i < n; i++) { x *= 10; sb.append((int) x); x -= (int) x; } return sb.toString(); } @Override public void print(float f) { super.print(dtos(f, 20)); } @Override public void println(float f) { super.println(dtos(f, 20)); } @Override public void print(double d) { super.print(dtos(d, 20)); } @Override public void println(double d) { super.println(dtos(d, 20)); } public void printlnArray(String[] array) { for (String i : array) super.println(i); } public void printSpace(Object... o) { int n = o.length - 1; for (int i = 0; i < n; i++) { super.print(o[i]); super.print(" "); } super.println(o[n]); } public void println(Object... o) { int n = o.length - 1; for (int i = 0; i < n; i++) super.print(o[i]); super.println(o[n]); } public void printYN(boolean o) { super.println(o ? "Yes" : "No"); } public void print(Object... o) { int n = o.length - 1; for (int i = 0; i < n; i++) super.print(o[i]); super.print(o[n]); } public void printArray(Object[] array) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(" "); } super.println(array[n]); } public void printArray(int[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printArray(int[] array) { this.printArray(array, " "); } public void printArray(Integer[] array) { this.printArray(array, " "); } public void printArray(Integer[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printlnArray(int[] array) { for (int i : array) super.println(i); } public void printArray(int[] array, String separator, java.util.function.IntUnaryOperator map) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(map.applyAsInt(array[i])); super.print(separator); } super.println(map.applyAsInt(array[n])); } public void printlnArray(int[] array, java.util.function.IntUnaryOperator map) { for (int i : array) super.println(map.applyAsInt(i)); } public void printlnArray(long[] array, java.util.function.LongUnaryOperator map) { for (long i : array) super.println(map.applyAsLong(i)); } public void printArray(int[] array, java.util.function.IntUnaryOperator map) { this.printArray(array, " ", map); } public void printArray(long[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printArray(long[] array) { this.printArray(array, " "); } public void printlnArray(long[] array) { for (long i : array) super.println(i); } public void printArray(double[] array) { printArray(array, " "); } public void printArray(double[] array, String separator) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(array[i]); super.print(separator); } super.println(array[n]); } public void printlnArray(double[] array) { for (double i : array) super.println(i); } public void printArray(boolean[] array, String a, String b) { int n = array.length - 1; for (int i = 0; i < n; i++) super.print((array[i] ? a : b) + " "); super.println(array[n] ? a : b); } public void printArray(boolean[] array) { this.printArray(array, "Y", "N"); } public void printArray(long[] array, String separator, java.util.function.LongUnaryOperator map) { int n = array.length - 1; for (int i = 0; i < n; i++) { super.print(map.applyAsLong(array[i])); super.print(separator); } super.println(map.applyAsLong(array[n])); } public void printArray(long[] array, java.util.function.LongUnaryOperator map) { this.printArray(array, " ", map); } public void printArray(ArrayList<?> array) { this.printArray(array, " "); } public void printArray(ArrayList<?> array, String separator) { int n = array.size() - 1; if (n == -1) return; for (int i = 0; i < n; i++) { super.print(array.get(i).toString()); super.print(separator); } super.println(array.get(n).toString()); } public void printlnArray(ArrayList<?> array) { int n = array.size(); for (int i = 0; i < n; i++) super.println(array.get(i).toString()); } public void printArray(int[][] array) { int n = array.length; if (n == 0) return; int m = array[0].length - 1; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) super.print(array[i][j] + " "); super.println(array[i][m]); } } public void printArray(long[][] array) { int n = array.length; if (n == 0) return; int m = array[0].length - 1; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) super.print(array[i][j] + " "); super.println(array[i][m]); } } public void printArray(boolean[][] array) { int n = array.length; if (n == 0) return; int m = array[0].length - 1; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) super.print(array[i][j] ? "○ " : "× "); super.println(array[i][m] ? "○" : "×"); } } public void printArray(char[][] array) { int n = array.length; if (n == 0) return; int m = array[0].length; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) super.print(array[i][j]); super.println(); } } }