結果
| 問題 | No.2670 Sum of Products of Interval Lengths |
| ユーザー |
 uwi
|
| 提出日時 | 2024-03-09 17:06:03 |
| 言語 | Java21 (openjdk 21) |
| 結果 |
AC
|
| 実行時間 | 1,093 ms / 2,000 ms |
| コード長 | 20,249 bytes |
| コンパイル時間 | 5,451 ms |
| コンパイル使用メモリ | 92,916 KB |
| 実行使用メモリ | 102,244 KB |
| 最終ジャッジ日時 | 2024-03-09 17:06:35 |
| 合計ジャッジ時間 | 25,000 ms |
|
ジャッジサーバーID （参考情報） |
judge12 / judge11 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1,022 ms
101,552 KB |
| testcase_01 | AC | 985 ms
98,188 KB |
| testcase_02 | AC | 1,006 ms
101,584 KB |
| testcase_03 | AC | 1,093 ms
102,240 KB |
| testcase_04 | AC | 1,090 ms
102,244 KB |
| testcase_05 | AC | 998 ms
101,584 KB |
| testcase_06 | AC | 969 ms
98,128 KB |
| testcase_07 | AC | 980 ms
101,556 KB |
| testcase_08 | AC | 963 ms
98,004 KB |
| testcase_09 | AC | 1,002 ms
101,552 KB |
| testcase_10 | AC | 999 ms
101,544 KB |
| testcase_11 | AC | 1,005 ms
101,548 KB |
| testcase_12 | AC | 1,007 ms
101,584 KB |
| testcase_13 | AC | 961 ms
101,564 KB |
| testcase_14 | AC | 984 ms
99,644 KB |
| testcase_15 | AC | 1,002 ms
101,548 KB |
| testcase_16 | AC | 1,018 ms
101,580 KB |
ソースコード
package contest240308;
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 G {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni();
long m = nl();
long[] w = new long[200005];
w[0] = 1;
w[1] = mod-1;
w[2] = 1;
long[] iw = inv(w);
long[] f = new long[200005];
for(int i = 1;i <= 200000;i++){
f[i] = Math.max(0, m-i+1) % mod * iw[i-1] % mod;
}
long[] res = inv(sub(new long[]{1}, f));
out.println(res[n]);
}
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 998244353
public 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;
}
///////////////////// 基本操作ここまで
// F_{t+1}(x) = -F_t(x)^2*P(x) + 2F_t(x)
// if want p-destructive, comment out flipping p just before returning.
public static long[] inv(long[] p) {
int n = p.length;
long[] f = {invl(p[0], mod)};
for (int i = 0; i < p.length; i++) {
if (p[i] == 0) continue;
p[i] = mod - p[i];
}
for (int i = 1; i < 2 * n; i *= 2) {
long[] f2 = mul(f, f, Math.min(n, 2 * i));
long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2 * i));
for (int j = 0; j < f.length; j++) {
f2p[j] += 2L * f[j];
if (f2p[j] >= mod) f2p[j] -= mod;
if (f2p[j] >= mod) f2p[j] -= mod;
}
f = f2p;
}
for (int i = 0; i < p.length; i++) {
if (p[i] == 0) continue;
p[i] = mod - p[i];
}
return f;
}
// differentiate
public static long[] d(long[] p) {
long[] q = new long[p.length];
for (int i = 0; i < p.length - 1; i++) {
q[i] = p[i + 1] * (i + 1) % mod;
}
return q;
}
// integrate
public static long[] i(long[] p) {
long[] q = new long[p.length];
for (int i = 0; i < p.length - 1; i++) {
q[i + 1] = p[i] * invl(i + 1, mod) % mod;
}
return q;
}
static long[] exp(long[] a) {
return exp(a, a.length);
}
/**
* https://cs.uwaterloo.ca/~eschost/publications/BoSc09-final.pdf
*
* @param a
* @param lim
* @return
* @verified https://judge.yosupo.jp/problem/exp_of_formal_power_series
*/
static long[] exp(long[] a, int lim) {
long[] F = {1L};
long[] G = {1L};
long[] da = d(a);
for (int m = 1; ; m *= 2) {
long[] G2 = mul(G, G, m);
G = sub(mul_(G, 2), mul(F, G2, m));
long[] Q = Arrays.copyOf(da, m - 1);
long[] W = add(Q, mul(G, sub(d(F), mul(F, Q, m), m - 1)));
F = mul(F, add(new long[]{1}, sub(Arrays.copyOf(a, m), i(W))), m);
if (m >= lim) break;
}
return Arrays.copyOf(F, lim);
}
public static long invl(long a, long mod) {
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 void main(String[] args) {
new G().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 1
public 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)); }
}