結果
問題 | No.2181 LRM Question 2 |
ユーザー | uwi |
提出日時 | 2023-01-06 23:44:27 |
言語 | Java21 (openjdk 21) |
結果 |
TLE
|
実行時間 | - |
コード長 | 20,683 bytes |
コンパイル時間 | 5,962 ms |
コンパイル使用メモリ | 101,220 KB |
実行使用メモリ | 125,500 KB |
最終ジャッジ日時 | 2024-11-30 20:46:09 |
合計ジャッジ時間 | 13,762 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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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 | 75 ms
57,576 KB |
testcase_01 | AC | 76 ms
50,880 KB |
testcase_02 | AC | 537 ms
53,216 KB |
testcase_03 | AC | 72 ms
51,032 KB |
testcase_04 | AC | 74 ms
51,092 KB |
testcase_05 | AC | 75 ms
53,076 KB |
testcase_06 | AC | 76 ms
51,200 KB |
testcase_07 | AC | 75 ms
51,064 KB |
testcase_08 | AC | 365 ms
53,212 KB |
testcase_09 | TLE | - |
testcase_10 | AC | 479 ms
53,632 KB |
testcase_11 | AC | 749 ms
53,408 KB |
testcase_12 | AC | 640 ms
53,356 KB |
testcase_13 | AC | 78 ms
51,648 KB |
testcase_14 | AC | 128 ms
55,948 KB |
testcase_15 | AC | 80 ms
51,068 KB |
testcase_16 | AC | 121 ms
55,828 KB |
testcase_17 | AC | 90 ms
51,448 KB |
testcase_18 | AC | 79 ms
51,344 KB |
testcase_19 | AC | 75 ms
51,460 KB |
testcase_20 | AC | 98 ms
53,876 KB |
testcase_21 | AC | 149 ms
52,152 KB |
testcase_22 | AC | 78 ms
51,112 KB |
testcase_23 | AC | 77 ms
51,128 KB |
testcase_24 | AC | 72 ms
50,752 KB |
testcase_25 | AC | 75 ms
125,500 KB |
ソースコード
package contest230106; import java.io.*; import java.util.*; import java.util.function.IntUnaryOperator; import java.util.function.LongUnaryOperator; public class G2 { InputStream is; FastWriter out; String INPUT = ""; public void solve() { cache.clear(); long L = nl(), R = nl(); int mod = ni(); // i < mod and n-(i+1) < modのときだけ非0 // i+1 > n-mod // n-mod-1 < i < mod // n-mod < mod // n < 2*mod // n^2*(n-1)^2*..*(n-i+1)^2 * (i+1)^2*...*n^2 // ------------------------------------------- // 1^2*2^2*...n^2 // n^2*(n-1)^2*..*(n-i+1)^2 // ------------------------------------------- // 1^2*2^2*...i^2 // C(n,i)^2 // sum_n sum_{i=1}^{n-1} C(n,i)^2 = (2n)!/(n!)^2-2 // (2n)(2n-1)(2n-2)...(n+1) // ------------------------- // n..........1 int[] primes = sieveEratosthenes(1000); int[][] F = factor(mod, primes); long ans = -2*(R-L+1); long gmod = 1; long gval = 0; for(int[] item : F){ fif = enumFIF(item[0]-1, item[0]); long mo = 1; for(int j = 0;j < item[1];j++){ mo = mo * item[0]; } long s = 0; for(int i = 0;i < R-L+1;i++){ long n = L+i; long val = C(2*n, n, item[0], item[1]); s += val; } s %= mo; gval = crt(gmod, gval, mo, s); gmod *= mo; } ans += gval; ans %= mod; if(ans < 0)ans += mod; out.println(ans); } static int[][] fif; 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 long crt(long p, long m, long q, long n) { assert p > 0; assert q > 0; assert 0 <= m; assert m < p; assert 0 <= n; assert n < q; if(p < q)return crt(q, n, p, m); long a = p, b = q; long pp = 1, qq = 0; while(b > 0){ long c = a / b; long d; d = a; a = b; b = d % b; d = pp; pp = qq; qq = d - c * qq; } if((n - m) % a != 0)return -1; long mod = p / a * q; // long ret = (p * pp % mod * ((n - m) / a) + m) % mod; long ret = ((n-m)*pp%q) * (p/a) + m; if(ret < 0)ret += mod; return ret; } 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 & 31); 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); } static Map<Integer, long[][]> cache = new HashMap<>(); public static long CY(long n, long r, int p, int[][] fif) { if(r < 0 || r > n)return 0; long ret = 1; for(;n > 0; n /= p, r /= p){ int np = (int)(n%p), rp = (int)(r%p); if(np < rp)return 0; int nrp = np-rp; if(nrp < 0)nrp += p; ret = ret*fif[0][np]%p*fif[1][rp]%p*fif[1][nrp]%p; } return ret; } 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 long C(long n, long r, int p, int q) { if(q == 1){ return CY(n, r, p, fif); } if(r < 0 || r > n)return 0; long P = 1; for(int i = 0;i < q;i++)P *= p; long z = n - r; long e0 = 0; for(long u = n/p;u > 0;u /= p)e0 += u; for(long u = r/p;u > 0;u /= p)e0 -= u; for(long u = z/p;u > 0;u /= p)e0 -= u; if(e0 >= q)return 0; // long em = 0; // for(long u = n/P*p;u > 0;u /= p)em += u; // for(long u = r/P*p;u > 0;u /= p)em -= u; // for(long u = z/P*p;u > 0;u /= p)em -= u; if(!cache.containsKey(p)){ long[] fact = new long[p*(q+1)+1]; long[] ifact = new long[p*(q+1)+1]; fact[0] = ifact[0] = 1; for(int i = 1;i <= p*(q+1);i++){ if(i % p == 0){ fact[i] = fact[i-1]; }else{ fact[i] = mul(fact[i-1], i, P); } ifact[i] = invl(fact[i], P); } cache.put(p, new long[][]{fact, ifact}); } long[] fact = cache.get(p)[0]; long[] ifact = cache.get(p)[1]; long num = 1; long den = 1; while(n > 0){ num = num * ff(n, p, q, fact, ifact) % P; den = den * ff(r, p, q, fact, ifact) * ff(z, p, q, fact, ifact) % P; n /= p; r /= p; z /= p; } long ret = num * invl(den, P) * pow(p, e0, P) % P; // if(!(p == 2 && q >= 3) && (em&1)==1){ // tr("kimasi"); // ret = (P-ret) % P; // } return ret; } static Map<Long, Long> cache2 = new HashMap<>(); public static long ff(long n, int p, int q, long[] fact, long[] ifact) { long code = n; code = code*1000000009 + p; code = code*1000000009 + q; if(cache2.containsKey(code))return cache2.get(code); long u = n/p; int v = (int)(n%p); boolean plused = q % 2 == 0; if(plused)q++; int r = (q-1)/2; long P = 1; for(int j = 1;j <= q;j++)P *= p; long PP = P / p * (p-1); // tr(n, p, q, u, v, r, P, PP); long ret = fact[v]; outer: for(int j = 1;j <= r;j++){ long[] betanums = new long[2*r+1]; long sign = 1; for(int i = -r;i <= r;i++){ if(i != j && -i != j){ if(u-i == 0)continue outer; betanums[i+r] = u-i; if(betanums[i+r] < 0){ sign *= -1; betanums[i+r] *= -1; } } } for(int i = -r;i <= r;i++){ if(i != j && -i != j){ long w = j-i; if(w < 0){ sign *= -1; w *= -1; } for(int k = 0;k <= 2*r;k++){ if(betanums[k] != 0){ long g = gcd(betanums[k], w); betanums[k] /= g; w /= g; } } if(w != 1){ // throw new AssertionError("dead"); } } } long beta = sign == -1 ? PP-1 : 1; for(int k = 0;k <= 2*r;k++){ if(betanums[k] > 0){ beta = mul(beta, betanums[k], PP); } } long po = pow(fact[j*p], beta, P); ret = mul(ret, po, P); } if(p == 2 && ((u*2%8 >= 3 && u*2%8 < 7) != (ret % 4 == 3)))ret = P-ret; outer2: for(int j = 1;j <= q-1;j++){ long cell = fact[j*p+v] * ifact[j*p] * ifact[v] % P; long[] alphanums = new long[q]; long sign = 1; for(int i = 0;i <= q-1;i++){ if(i != j){ alphanums[i] = u-i; if(u-i == 0)continue outer2; if(alphanums[i] < 0){ sign *= -1; alphanums[i] *= -1; } } } for(int i = 0;i <= q-1;i++){ if(i != j){ long w = j-i; if(w < 0){ sign *= -1; w *= -1; } for(int k = 0;k <= q-1;k++){ if(alphanums[k] != 0){ long g = gcd(alphanums[k], w); alphanums[k] /= g; w /= g; } } if(w != 1){ // throw new AssertionError("dead2"); } } } long alpha = sign == -1 ? PP-1 : 1; for(int k = 0;k <= q-1;k++){ if(alphanums[k] > 0){ alpha = alpha * (alphanums[k] % PP) % PP; } } // tr("alpha", j, r, cell, alpha); // System.err.println(alpha + " " + P + " " + PP); ret = ret * pow(cell, alpha, P) % P; } if(plused){ cache2.put(code, ret % (P/p)); return ret % (P/p); }else{ cache2.put(code, ret); return ret; } } public static long gcd(long a, long b) { while (b > 0) { long c = a; a = b; b = c % b; } return a; } public static long mul(long a, long b, long mod) { return a*b%mod; // if(a >= mod || a < 0)a %= mod; // if(a < 0)a += mod; // if(b >= mod || b < 0)b %= mod; // if(b < 0)b += mod; // // long ret = 0; // int x = 63-Long.numberOfLeadingZeros(b); // for(;x >= 0;x--){ // ret += ret; // if(ret >= mod)ret -= mod; // if(b<<~x<0){ // ret += a; // if(ret >= mod)ret -= mod; // } // } // return ret; } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x--) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } 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 void main(String[] args) { new G2().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)); } }