結果
問題 | No.2181 LRM Question 2 |
ユーザー |
|
提出日時 | 2023-01-07 01:23:22 |
言語 | Java (openjdk 23) |
結果 |
AC
|
実行時間 | 1,511 ms / 2,000 ms |
コード長 | 18,599 bytes |
コンパイル時間 | 5,579 ms |
コンパイル使用メモリ | 94,528 KB |
実行使用メモリ | 45,348 KB |
最終ジャッジ日時 | 2024-11-30 22:18:08 |
合計ジャッジ時間 | 15,209 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 23 |
ソースコード
package contest230106;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 G5 {InputStream is;FastWriter out;String INPUT = "";public void solve(){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..........1CombinationGeneralMultipleSmall cgm = new CombinationGeneralMultipleSmall(mod);long ans = -2*(R-L+1);long s = 0;for(int i = 0;i < R-L+1;i++){long n = L+i;// long val = cgm.C(2*n, n);long val = cgm.Center(n);s += val;}ans += s;ans %= mod;if(ans < 0)ans += mod;out.println(ans);}public static class CombinationGeneralMultipleSmall {int[][] f;long[][] pesmap;int[] qmap;long[][] aprs;public CombinationGeneralMultipleSmall(int mod){int[] primes = sieveEratosthenes((int)Math.sqrt(mod));f = factor(mod, primes);pesmap = new long[f.length][];qmap = new int[f.length];for(int j = 0;j < f.length;j++){int[] u = f[j];int P = u[0], e = u[1];int Q = (int)Math.pow(P, e);long[] pes = new long[Q];pes[0] = 1;for(int i = 1;i < Q;i++){if(i % P == 0){pes[i] = pes[i-1];}else{pes[i] = pes[i-1] * i % Q;}}pesmap[j] = pes;qmap[j] = Q;}aprs = aprs(qmap);}public long C(long n, long m){if(m < 0 || m > n)return 0L;long[] mods = new long[f.length];for(int i = 0;i < f.length;i++){mods[i] = C(n, m, i);}return crt(qmap, mods, aprs);}private long C(long n, long m, int pind){if(m < 0 || m > n)return 0L;int P = f[pind][0], e = f[pind][1];long pe = 0;int mod = qmap[pind];long num = 1;long den = 1;for(long x = n;x > 0;x /= P){num = num * F(x, pind) % mod;pe += x/P;}for(long x = m;x > 0;x /= P){den = den * F(x, pind) % mod;pe -= x/P;}for(long x = n-m;x > 0;x /= P){den = den * F(x, pind) % mod;pe -= x/P;}if(pe >= e)return 0L;num = num * invl(den, mod) % mod;for(int i = 0;i < pe;i++){num = num * P % mod;}// System.err.println(Arrays.toString(new long[]{n, m, P, e, num}));return num;}public long Center(long n){long[] mods = new long[f.length];for(int i = 0;i < f.length;i++){mods[i] = Center(n, i);}return crt(qmap, mods, aprs);}private long Center(long n, int pind){int P = f[pind][0], e = f[pind][1];long pe = 0;int mod = qmap[pind];long num = 1;long den = 1;for(long x = 2*n;x > 0;x /= P){num = num * F(x, pind) % mod;pe += x/P;}long minus = 0;for(long x = n;x > 0;x /= P){den = den * F(x, pind) % mod;minus += x/P;}pe -= 2*minus;den = den * den % mod;if(pe >= e)return 0L;num = num * invl(den, mod) % mod;for(int i = 0;i < pe;i++){num = num * P;}num %= mod;return num;}public static long[][] aprs(int[] divs){if(divs.length == 0)return null;long div = divs[0];long[][] ret = new long[divs.length][];for(int i = 1;i < divs.length;i++){ret[i] = exgcd(div, divs[i]);div = div * divs[i];}return ret;}public static long crt(final int[] divs, final long[] mods, long[][] aprs){if(divs.length == 0)return 0L;long div = divs[0];long mod = mods[0];for(int i = 1;i < divs.length;i++){long[] apr = aprs[i];long ndiv = div * divs[i];mod += ((mods[i]-mod)*apr[1]%divs[i]) * div;div = ndiv;}mod %= div;if(mod < 0)mod += div;return mod;}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 long FNaive(int n, int P, int e){long mod = 1;for(int i = 0;i < e;i++)mod = mod * P;long ret = 1;for(int i = 1;i <= n;i++){if(i % P == 0)continue;ret = ret * i % mod;}return ret;}public long F(long n, int pind){int mod = qmap[pind];long[] pes = pesmap[pind];assert pes[mod-1] == 1 || pes[mod-1] == mod-1;long ret = pes[(int)(n%mod)];if(pes[mod-1] == mod-1 && n/mod%2 == 1){ret = mod-ret;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 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 & 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=nint[] 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) {new G5().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)); }}