結果

問題 No.2181 LRM Question 2
ユーザー 37zigen
提出日時 2022-10-14 20:43:38
言語 Java
(openjdk 23)
結果
AC  
実行時間 1,883 ms / 2,000 ms
コード長 5,509 bytes
コンパイル時間 2,732 ms
コンパイル使用メモリ 82,000 KB
実行使用メモリ 54,048 KB
最終ジャッジ日時 2024-06-26 12:45:24
合計ジャッジ時間 14,119 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.NoSuchElementException;
public class Main implements Runnable {
    public static void main(String[] args) {
//      new Thread(null, new Main(), "", Runtime.getRuntime().maxMemory()).start();
        new Main().run();
    }
    
    long pow(long a, long n) {
        if (n == 0) return 1;
        return pow(a*a,n/2)*(n%2==1?a:1);
    }
    
    long pow_mod(long a, long n, long mod) {
        a %= mod;
        if (n == 0) return 1;
        return pow_mod(a * a % mod, n / 2, mod) * (n % 2 == 1 ? a : 1) % mod;
    }
    
    long inv(long a, long mod, long ord) {
        return pow_mod(a, ord-1, mod);
    }
    
    long gcd(long a, long b) {
        if (a == 0) return b;
        else return gcd(b % a, a);
    }
    
    public void run() {
        FastScanner sc = new FastScanner();
        PrintWriter pw=new PrintWriter(System.out);
        long L = sc.nextLong();
        long R = sc.nextLong();
        long M = sc.nextLong();
        pw.println(solve(L, R, M));
        pw.close();
    }
    
    long[][] rec = new long[100][100];
    void init() {
        for (int i = 0; i < rec.length; ++i) {
            for (int j = 0; j < rec[i].length; ++j) {
                rec[i][j] = -1;
            }
        }
    }
    
    long c(long n, long k, long mod) {
        if (k<0||n-k<0) return 0;
        if (k == 0 || k == n) return 1;
        if (rec[(int)n][(int)k] != -1) return rec[(int)n][(int)k];
        return rec[(int)n][(int)k] = (c(n-1, k, mod) + c(n-1, k-1, mod))%mod;
    }
    
    long exact(long L, long R, long M) {
        init();
        long ret = 0;
        for (long n = L; n <= R; ++n) {
            ret = (ret + c(2 * n, n, M))% M;
        }
        ret = (ret % M + M) % M;
        return ret;
    }
    
    long coprime(long a, long m) {
        while (gcd(a, m) != 1) {
            a /= gcd(a, m);
        }
        return a;
    }
    
    List<ArrayList<? extends Number>> factor(long n) {
        ArrayList<Long> primes = new ArrayList<>();
        ArrayList<Integer> indexes = new ArrayList<>();
        for (long i = 2; i * i <= n; ++i) {
            int e = 0;
            while (n % i == 0) {
                n /= i;
                ++e;
            }
            if (e != 0) {
                primes.add(i);
                indexes.add(e);
            }
        }
        if (n != 1) {
            primes.add(n);
            indexes.add(1);
        }
        return List.of(primes, indexes);
    }
    
    long solve(long L, long R, long M) {
        if (M == 1) return 0;
        var factor = factor(M);
        ArrayList<Long> primes = (ArrayList<Long>) factor.get(0);
        ArrayList<Integer> indexes = (ArrayList<Integer>) factor.get(1);
        ArrayList<Long> pes = new ArrayList<>();
        for (int i = 0; i < primes.size(); ++i) pes.add(pow(primes.get(i), indexes.get(i)));
        long[] v = new long[primes.size()];
        for (int i = 0; i < primes.size(); ++i) {
            int p = primes.get(i).intValue();
            int pe = (int) pow(primes.get(i), indexes.get(i));
            long[] fac = new long[pe + 1];
            long[] ifac = new long[fac.length];
            Arrays.fill(fac, 1);
            Arrays.fill(ifac, 1);
            for (int j = 1; j < fac.length; ++j) fac[j] = (j % p == 0 ? 1 : j ) * fac[j - 1] % pe;
            ifac[fac.length - 1] = fac[fac.length - 1];
            for (int j = ifac.length - 1; j >= 1; --j) ifac[j - 1] = (j % p == 0 ? 1 : j ) * ifac[j] % pe;
            for (long n = L; n <= R; ++n) {
                long comb = 1;
                long e = 0;
                long f = 0;
                {
                    long a = 2 * n;
                    long b = n;
                    do {
                        comb = comb * fac[(int) (a%pe)] % pe * ifac[(int) (b%pe)] % pe * ifac[(int) (b%pe)] % pe;
                        f += a / pe - b / pe * 2;
                        e += a / p - b / p * 2;
                        a /= p;
                        b /= p;
                    } while (a != 0);
                }
                e = Math.min(e, indexes.get(i));
                comb = comb * pow_mod(p, e, pe);
                comb = comb * (f % 2 == 1 ? fac[fac.length - 1] : 1);
                v[i] = (v[i] + comb) % pe;
            }
        }
        for (long i = 0; i < M; ++i) {
            boolean ok = true;
            for (int j = 0; j < primes.size() && ok; ++j) {
                ok &= v[j] == i % pes.get(j);
            }
            if (ok) {
                long ans = i - 2 * (R - L + 1);
                ans = (ans % M + M) % M;
                return ans;
            }
        }
        throw new AssertionError();
    }
    
    void tr(Object... objects) {
        System.err.println(Arrays.deepToString(objects));
    }
    
}
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }
    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }
    private void skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
    }
    public boolean hasNext() {
        skipUnprintable();
        return hasNextByte();
    }
    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        return (int) nextLong();
    }
}
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