結果
| 問題 | No.2499 Sum of Products of Sums |
| ユーザー |
 uwi
|
| 提出日時 | 2023-10-10 02:59:48 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 573 ms / 2,000 ms |
| コード長 | 19,007 bytes |
| コンパイル時間 | 5,921 ms |
| コンパイル使用メモリ | 94,492 KB |
| 実行使用メモリ | 59,932 KB |
| 最終ジャッジ日時 | 2024-09-13 00:12:04 |
| 合計ジャッジ時間 | 11,169 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 17 |
ソースコード
package contest231006;import java.io.*;import java.util.ArrayDeque;import java.util.Arrays;import java.util.InputMismatchException;import java.util.Queue;import java.util.function.IntUnaryOperator;import java.util.function.LongUnaryOperator;public class H {InputStream is;FastWriter out;String INPUT = "";public void solve(){// W!*sum_{sum t_k = W} \prod (C(b_k+W,W+t_k) - C(a_k+W-1,W+t_k)) / t_k!int H = ni(), W = ni();int[][] ab = nmi(H, 2);int[][] fif = enumFIF(1000, mod);long[] ans = {fif[0][W]};for(int i = 0;i < H;i++){int a = ab[i][0], b = ab[i][1];long[] csb = cs(b+W, W+W);long[] csa = cs(a+W-1, W+W);long[] c = new long[W+1];for(int j = 0;j <= W;j++){c[j] = (csb[W+j] - csa[W+j] + mod) * fif[1][j] % mod;}ans = mul(ans, c, W+1);}out.println(ans[W]);}static long[] cs(int n, int K){long[] ret = new long[K+1];if(n < 0)return ret;ret[0] = 1;long h = n%mod;int[] invs = enumInvs(K+1, mod);for(int i = 1;i <= K;i++, h--){ret[i] = ret[i-1] * h % mod * invs[i] % mod;}return ret;}public static int[] enumInvs(int n, int mod) {int[] inv = new int[n + 1];inv[1] = 1;for (int i = 2; i <= n; i++) {inv[i] = (int) (inv[mod % i] * (long) (mod - mod / i) % mod);}return inv;}public static int[][] enumFIF(int n, int mod) {int[] f = new int[n + 1];int[] invf = new int[n + 1];f[0] = 1;for (int i = 1; i <= n; i++) {f[i] = (int) ((long) f[i - 1] * i % mod);}long a = f[n];long b = mod;long p = 1, q = 0;while (b > 0) {long c = a / b;long d;d = a;a = b;b = d % b;d = p;p = q;q = d - c * q;}invf[n] = (int) (p < 0 ? p + mod : p);for (int i = n - 1; i >= 0; i--) {invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);}return new int[][]{f, invf};}public static class NTTStockham998244353 {private static final int P = 998244353, mod = P, G = 3;private static long[] wps;public static long[] convolve(long[] a, long[] b){int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);wps = new long[m];long unit = pow(G, (P-1)/m);wps[0] = 1;for(int p = 1;p < m;p++) {wps[p] = wps[p-1] * unit % mod;}long[] fa = go(a, m, false);long[] fb = a == b ? fa : go(b, m, false);for(int i = 0;i < m;i++){fa[i] = fa[i]*fb[i] % mod;}fa = go(fa, m, true);for(int i = 1, j = m-1;i < j;i++,j--) {long d = fa[i]; fa[i] = fa[j]; fa[j] = d;}return fa;}private static void fft(long[] X, long[] Y){int s = 1;boolean eo = false;for(int n = X.length;n >= 4;n /= 2) {int m = n/2;for(int p = 0;p < m;p++) {long wp = wps[s*p];long wk = (wp<<32)/P;for(int q = 0;q < s;q++) {long a = X[q + s*(p+0)];long b = X[q + s*(p+m)];long ndsts = a + b;if(ndsts >= 2*P)ndsts -= 2*P;long T = a - b + 2*P;long Q = wk*T>>>32;Y[q + s*(2*p+0)] = ndsts;Y[q + s*(2*p+1)] = wp*T-Q*P&(1L<<32)-1;}}s *= 2;eo = !eo;long[] D = X; X = Y; Y = D;}long[] z = eo ? Y : X;for(int q = 0;q < s;q++) {long a = X[q + 0];long b = X[q + s];z[q+0] = (a+b) % P;z[q+s] = (a-b+2*P) % P;}}// private static void fft(long[] X, long[] Y)// {// int s = 1;// boolean eo = false;// for(int n = X.length;n >= 4;n /= 2) {// int m = n/2;// for(int p = 0;p < m;p++) {// long wp = wps[s*p];// for(int q = 0;q < s;q++) {// long a = X[q + s*(p+0)];// long b = X[q + s*(p+m)];// Y[q + s*(2*p+0)] = (a+b) % P;// Y[q + s*(2*p+1)] = (a-b+P) * wp % P;// }// }// s *= 2;// eo = !eo;// long[] D = X; X = Y; Y = D;// }// long[] z = eo ? Y : X;// for(int q = 0;q < s;q++) {// long a = X[q + 0];// long b = X[q + s];// z[q+0] = (a+b) % P;// z[q+s] = (a-b+P) % P;// }// }private static long[] go(long[] src, int n, boolean inverse){long[] dst = Arrays.copyOf(src, n);fft(dst, new long[n]);if(inverse){long in = invl(n);for(int i = 0;i < n;i++){dst[i] = dst[i] * in % mod;}}return dst;}private static long pow(long a, long n) {// a %= mod;long ret = 1;int x = 63 - Long.numberOfLeadingZeros(n);for (; x >= 0; x--) {ret = ret*ret % mod;if (n<<~x<0)ret = ret*a%mod;}return ret;}private static long invl(long a) {long b = mod;long p = 1, q = 0;while (b > 0) {long c = a / b;long d;d = a;a = b;b = d % b;d = p;p = q;q = d - c * q;}return p < 0 ? p + mod : p;}}public static final int mod = 998244353;public static final int G = 3;// only 998244353public static long[] mul(long[] a, long[] b){if(a.length == 0 && b.length == 0)return new long[0];if(a.length + b.length >= 300) {return Arrays.copyOf(NTTStockham998244353.convolve(a, b), a.length + b.length - 1);}else{return mulnaive(a, b);}}public static long[] mul(long[] a, long[] b, int lim){if(a.length + b.length >= 300) {return Arrays.copyOf(NTTStockham998244353.convolve(a, b), lim);}else{return mulnaive(a, b, lim);}}// public static final int mod = 1000000007;// public static long[] mul(long[] a, long[] b)// {// if(Math.max(a.length, b.length) >= 3000){// return Arrays.copyOf(NTTCRT.convolve(a, b, 3, mod), a.length+b.length-1);// }else{// return mulnaive(a, b);// }// }// public static long[] mul(long[] a, long[] b, int lim)// {// if(Math.max(a.length, b.length) >= 3000){// return Arrays.copyOf(NTTCRT.convolve(a, b, 3, mod), lim);// }else{// return mulnaive(a, b, lim);// }// }public static final long big = (Long.MAX_VALUE/mod/mod-1)*mod*mod;public static long[] mulnaive(long[] a, long[] b){long[] c = new long[a.length+b.length-1];for(int i = 0;i < a.length;i++){for(int j = 0;j < b.length;j++){c[i+j] += a[i]*b[j];if(c[i+j] >= big)c[i+j] -= big;}}for(int i = 0;i < c.length;i++)c[i] %= mod;return c;}public static long[] mulnaive(long[] a, long[] b, int lim){long[] c = new long[lim];for(int i = 0;i < a.length;i++){for(int j = 0;j < b.length && i+j < lim;j++){c[i+j] += a[i]*b[j];if(c[i+j] >= big)c[i+j] -= big;}}for(int i = 0;i < c.length;i++)c[i] %= mod;return c;}public static long[] mul_(long[] a, long k){for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod;return a;}public static long[] mul(long[] a, long k){a = Arrays.copyOf(a, a.length);for(int i = 0;i < a.length;i++)a[i] = a[i] * k % mod;return a;}public static long[] add(long[] a, long[] b){long[] c = new long[Math.max(a.length, b.length)];for(int i = 0;i < a.length;i++)c[i] += a[i];for(int i = 0;i < b.length;i++)c[i] += b[i];for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;return c;}public static long[] add(long[] a, long[] b, int lim){long[] c = new long[lim];for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i];for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;return c;}public static long[] sub(long[] a, long[] b){long[] c = new long[Math.max(a.length, b.length)];for(int i = 0;i < a.length;i++)c[i] += a[i];for(int i = 0;i < b.length;i++)c[i] -= b[i];for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;return c;}public static long[] sub(long[] a, long[] b, int lim){long[] c = new long[lim];for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i];for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;return c;}public static void main(String[] args) {new H().run();}public void run(){long S = System.currentTimeMillis();is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());out = new FastWriter(System.out);solve();out.flush();long G = System.currentTimeMillis();tr(G-S+"ms");// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){// @Override// public void run() {// long s = System.currentTimeMillis();// solve();// out.flush();// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");// }// };// t.start();// t.join();}private boolean eof(){if(lenbuf == -1)return true;int lptr = ptrbuf;while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;try {is.mark(1000);while(true){int b = is.read();if(b == -1){is.reset();return true;}else if(!isSpaceChar(b)){is.reset();return false;}}} catch (IOException e) {return true;}}private final byte[] inbuf = new byte[1024];public int lenbuf = 0, ptrbuf = 0;private int readByte(){if(lenbuf == -1)throw new InputMismatchException();if(ptrbuf >= lenbuf){ptrbuf = 0;try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }if(lenbuf <= 0)return -1;}return inbuf[ptrbuf++];}private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }// private boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }private double nd() { return Double.parseDouble(ns()); }private char nc() { return (char)skip(); }private String ns(){int b = skip();StringBuilder sb = new StringBuilder();while(!(isSpaceChar(b))){sb.appendCodePoint(b);b = readByte();}return sb.toString();}private char[] ns(int n){char[] buf = new char[n];int b = skip(), p = 0;while(p < n && !(isSpaceChar(b))){buf[p++] = (char)b;b = readByte();}return n == p ? buf : Arrays.copyOf(buf, p);}private char[][] nm(int n, int m){char[][] map = new char[n][];for(int i = 0;i < n;i++)map[i] = ns(m);return map;}private int[][] nmi(int n, int m){int[][] map = new int[n][];for(int i = 0;i < n;i++)map[i] = na(m);return map;}private int[] na(int n){int[] a = new int[n];for(int i = 0;i < n;i++)a[i] = ni();return a;}private long[] nal(int n){long[] a = new long[n];for(int i = 0;i < n;i++)a[i] = nl();return a;}private int ni(){int num = 0, b;boolean minus = false;while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));if(b == '-'){minus = true;b = readByte();}while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = readByte();}}private long nl(){long num = 0;int b;boolean minus = false;while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));if(b == '-'){minus = true;b = readByte();}while(true){if(b >= '0' && b <= '9'){num = num * 10 + (b - '0');}else{return minus ? -num : num;}b = readByte();}}public static class FastWriter{private static final int BUF_SIZE = 1<<13;private final byte[] buf = new byte[BUF_SIZE];private final OutputStream out;private int ptr = 0;private FastWriter(){out = null;}public FastWriter(OutputStream os){this.out = os;}public FastWriter(String path){try {this.out = new FileOutputStream(path);} catch (FileNotFoundException e) {throw new RuntimeException("FastWriter");}}public FastWriter write(byte b){buf[ptr++] = b;if(ptr == BUF_SIZE)innerflush();return this;}public FastWriter write(char c){return write((byte)c);}public FastWriter write(char[] s){for(char c : s){buf[ptr++] = (byte)c;if(ptr == BUF_SIZE)innerflush();}return this;}public FastWriter write(String s){s.chars().forEach(c -> {buf[ptr++] = (byte)c;if(ptr == BUF_SIZE)innerflush();});return this;}private static int countDigits(int l) {if (l >= 1000000000) return 10;if (l >= 100000000) return 9;if (l >= 10000000) return 8;if (l >= 1000000) return 7;if (l >= 100000) return 6;if (l >= 10000) return 5;if (l >= 1000) return 4;if (l >= 100) return 3;if (l >= 10) return 2;return 1;}public FastWriter write(int x){if(x == Integer.MIN_VALUE){return write((long)x);}if(ptr + 12 >= BUF_SIZE)innerflush();if(x < 0){write((byte)'-');x = -x;}int d = countDigits(x);for(int i = ptr + d - 1;i >= ptr;i--){buf[i] = (byte)('0'+x%10);x /= 10;}ptr += d;return this;}private static int countDigits(long l) {if (l >= 1000000000000000000L) return 19;if (l >= 100000000000000000L) return 18;if (l >= 10000000000000000L) return 17;if (l >= 1000000000000000L) return 16;if (l >= 100000000000000L) return 15;if (l >= 10000000000000L) return 14;if (l >= 1000000000000L) return 13;if (l >= 100000000000L) return 12;if (l >= 10000000000L) return 11;if (l >= 1000000000L) return 10;if (l >= 100000000L) return 9;if (l >= 10000000L) return 8;if (l >= 1000000L) return 7;if (l >= 100000L) return 6;if (l >= 10000L) return 5;if (l >= 1000L) return 4;if (l >= 100L) return 3;if (l >= 10L) return 2;return 1;}public FastWriter write(long x){if(x == Long.MIN_VALUE){return write("" + x);}if(ptr + 21 >= BUF_SIZE)innerflush();if(x < 0){write((byte)'-');x = -x;}int d = countDigits(x);for(int i = ptr + d - 1;i >= ptr;i--){buf[i] = (byte)('0'+x%10);x /= 10;}ptr += d;return this;}public FastWriter write(double x, int precision){if(x < 0){write('-');x = -x;}x += Math.pow(10, -precision)/2;// if(x < 0){ x = 0; }write((long)x).write(".");x -= (long)x;for(int i = 0;i < precision;i++){x *= 10;write((char)('0'+(int)x));x -= (int)x;}return this;}public FastWriter writeln(char c){ return write(c).writeln(); }public FastWriter writeln(int x){ return write(x).writeln(); }public FastWriter writeln(long x){ return write(x).writeln(); }public FastWriter writeln(double x, int precision){ return write(x, precision).writeln(); }public FastWriter write(int... xs){boolean first = true;for(int x : xs) {if (!first) write(' ');first = false;write(x);}return this;}public FastWriter write(long... xs){boolean first = true;for(long x : xs) {if (!first) write(' ');first = false;write(x);}return this;}public FastWriter write(IntUnaryOperator f, int... xs){boolean first = true;for(int x : xs) {if (!first) write(' ');first = false;write(f.applyAsInt(x));}return this;}public FastWriter write(LongUnaryOperator f, long... xs){boolean first = true;for(long x : xs) {if (!first) write(' ');first = false;write(f.applyAsLong(x));}return this;}public FastWriter writeln(){return write((byte)'\n');}public FastWriter writeln(int... xs) { return write(xs).writeln(); }public FastWriter writeln(long... xs) { return write(xs).writeln(); }public FastWriter writeln(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, xs).writeln(); }public FastWriter writeln(char[] line) { return write(line).writeln(); }public FastWriter writeln(char[]... map) { for(char[] line : map)write(line).writeln();return this; }public FastWriter writeln(String s) { return write(s).writeln(); }private void innerflush(){try {out.write(buf, 0, ptr);ptr = 0;} catch (IOException e) {throw new RuntimeException("innerflush");}}public void flush(){innerflush();try {out.flush();} catch (IOException e) {throw new RuntimeException("flush");}}public FastWriter print(byte b) { return write(b); }public FastWriter print(char c) { return write(c); }public FastWriter print(char[] s) { return write(s); }public FastWriter print(String s) { return write(s); }public FastWriter print(int x) { return write(x); }public FastWriter print(long x) { return write(x); }public FastWriter print(double x, int precision) { return write(x, precision); }public FastWriter println(char c){ return writeln(c); }public FastWriter println(int x){ return writeln(x); }public FastWriter println(long x){ return writeln(x); }public FastWriter println(double x, int precision){ return writeln(x, precision); }public FastWriter print(int... xs) { return write(xs); }public FastWriter print(long... xs) { return write(xs); }public FastWriter print(IntUnaryOperator f, int... xs) { return write(f, xs); }public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }public FastWriter println(int... xs) { return writeln(xs); }public FastWriter println(long... xs) { return writeln(xs); }public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, xs); }public FastWriter println(char[] line) { return writeln(line); }public FastWriter println(char[]... map) { return writeln(map); }public FastWriter println(String s) { return writeln(s); }public FastWriter println() { return writeln(); }}public static void trnz(int... o){for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");System.out.println();}// print ids which are 1public static void trt(long... o){Queue<Integer> stands = new ArrayDeque<>();for(int i = 0;i < o.length;i++){for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));}System.out.println(stands);}public static void tf(boolean... r){for(boolean x : r)System.out.print(x?'#':'.');System.out.println();}public static void tf(boolean[]... b){for(boolean[] r : b) {for(boolean x : r)System.out.print(x?'#':'.');System.out.println();}System.out.println();}public void tf(long[]... b){if(INPUT.length() != 0) {for (long[] r : b) {for (long x : r) {for (int i = 0; i < 64; i++) {System.out.print(x << ~i < 0 ? '#' : '.');}}System.out.println();}System.out.println();}}public void tf(long... b){if(INPUT.length() != 0) {for (long x : b) {for (int i = 0; i < 64; i++) {System.out.print(x << ~i < 0 ? '#' : '.');}}System.out.println();}}private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }}