結果
問題 | No.109 N! mod M |
ユーザー | uwi |
提出日時 | 2015-01-16 23:45:19 |
言語 | Java21 (openjdk 21) |
結果 |
WA
|
実行時間 | - |
コード長 | 6,471 bytes |
コンパイル時間 | 2,197 ms |
コンパイル使用メモリ | 90,332 KB |
実行使用メモリ | 52,876 KB |
最終ジャッジ日時 | 2024-06-22 12:25:46 |
合計ジャッジ時間 | 4,911 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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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 | 67 ms
50,976 KB |
testcase_01 | AC | 254 ms
52,876 KB |
testcase_02 | AC | 183 ms
52,760 KB |
testcase_03 | AC | 71 ms
50,900 KB |
testcase_04 | AC | 102 ms
51,312 KB |
testcase_05 | AC | 1,149 ms
52,532 KB |
testcase_06 | AC | 79 ms
50,996 KB |
testcase_07 | WA | - |
testcase_08 | AC | 73 ms
51,020 KB |
ソースコード
import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class Main { static InputStream is; static PrintWriter out; static String INPUT = ""; static void solve() { int[] primes = sieveEratosthenes(100000); for(int T = ni();T >= 1;T--){ int n = ni(), m = ni(); if(n <= 500000){ long ret = 1; for(int i = 1;i <= n;i++){ ret = ret * i % m; } out.println(ret); }else{ int[][] f = factor(m, primes); long div = 1, res = 0; for(int[] fp : f){ long lres = ff(n, fp[0], fp[1]); long lmul = 1; for(int i = 0;i < fp[1];i++)lmul *= fp[0]; res = crt(lmul, lres, div, res); div *= lmul; } out.println(res); } } } static long ff(int n, int p, int e) { if(n >= (long)p*e)return 0; if(e >= 2)throw new RuntimeException(); long ret = p-1; for(int i = p-1;i >= n+1;i--){ ret = ret * invl(i, p) % p; } return ret; } 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 long[] exgcd(long a, long b) { if(a == 0 || b == 0)return null; int as = Long.signum(a); int bs = Long.signum(b); a = Math.abs(a); b = Math.abs(b); long p = 1, q = 0, r = 0, s = 1; while(b > 0){ long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; d = r; r = s; s = d - c * s; } return new long[]{a, p * as, r * bs}; } public static long crt(long p, long m, long q, long n) { long[] apr = exgcd(p, q); if((n - m) % apr[0] != 0)return -1; long mod = p * (q / apr[0]); long a = (apr[1] * ((n - m) / apr[0]) * p + m) % mod; if(a < 0)a += mod; return a; } public static int[][] factor(int n, int[] primes) { int[][] ret = new int[9][2]; int rp = 0; for(int p : primes){ if(p * p > n)break; int i; for(i = 0;n % p == 0;n /= p, i++); if(i > 0){ ret[rp][0] = p; ret[rp][1] = i; rp++; } } if(n != 1){ ret[rp][0] = n; ret[rp][1] = 1; rp++; } return Arrays.copyOf(ret, rp); } public static int[] sieveEratosthenes(int n) { if(n <= 32){ int[] primes = {2,3,5,7,11,13,17,19,23,29,31}; for(int i = 0;i < primes.length;i++){ if(n < primes[i]){ return Arrays.copyOf(primes, i); } } return primes; } int u = n+32; double lu = Math.log(u); int[] ret = new int[(int)(u/lu+u/lu/lu*1.5)]; ret[0] = 2; int pos = 1; int[] isnp = new int[(n+1)/32/2+1]; int sup = (n+1)/32/2+1; int[] tprimes = {3,5,7,11,13,17,19,23,29,31}; for(int tp : tprimes){ ret[pos++] = tp; int[] ptn = new int[tp]; for(int i = (tp-3)/2;i < tp<<5;i+=tp)ptn[i>>5] |= 1<<i; for(int j = 0;j < sup;j += tp){ for(int i = 0;i < tp && i+j < sup;i++){ isnp[j+i] |= ptn[i]; } } } // 3,5,7 // 2x+3=n int[] magic = {0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14}; int h = n/2; for(int i = 0;i < sup;i++){ for(int j = ~isnp[i];j != 0;j &= j-1){ int pp = i<<5|magic[(j&-j)*0x076be629>>>27]; int p = 2*pp+3; if(p > n)break; ret[pos++] = p; if((long)p*p > n)continue; for(int q = (p*p-3)/2;q <= h;q += p)isnp[q>>5] |= 1<<q; } } return Arrays.copyOf(ret, pos); } public static void main(String[] args) throws Exception { long S = System.currentTimeMillis(); is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); solve(); out.flush(); long G = System.currentTimeMillis(); tr(G-S+"ms"); } private static 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 static byte[] inbuf = new byte[1024]; static int lenbuf = 0, ptrbuf = 0; private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private static double nd() { return Double.parseDouble(ns()); } private static char nc() { return (char)skip(); } private static String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private static 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 static 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 static int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private static 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 static 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(); } } private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); } }