小nm:I

import java.util.*;

public class Main {

    static final int N = 2010, MOD = (int) 1e9 + 7;
    static int[][] C = new int[N][N];
    static int n;

    public static void main(String[] args) {

        init();

        Scanner sc = new Scanner(System.in);

        n = sc.nextInt();

        while (n -- > 0) {
            int i = sc.nextInt(), j = sc.nextInt();

            System.out.println(C[i][j]);
        }
    }

    static void init() {
        for (int i = 0; i < N; i++)
            for (int j = 0; j <= i; j++) {
                if (j == 0) C[i][j] = 1;
                else C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % MOD;
            }
    }
}

大nm:II

import java.util.Scanner;

public class Main {
    static final int N = (int)1e7 + 10, mod = (int)1e9 + 7;
    static long[] high = new long[N], low = new long[N];

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        //预处理
        high[0] = 1; low[0] = 1;
        for (int i = 1; i < N; i++) {
            high[i] = high[i - 1] * i % mod;
            low[i] = quick_mi(high[i], mod - 2, mod);
        }
        int q = sc.nextInt();
        while (q -- > 0) {
            int n = sc.nextInt(), m = sc.nextInt();
            System.out.println(C(n, m));
        }

        sc.close();
    }

    static long C(int n, int m) {
        return high[n] * low[m] % mod * low[n - m] % mod;
    }

    static long quick_mi(long a, long k, long q) {
        long res = 1;
        while (k != 0) {
            if ((k & 1) == 1) res = res * a % q;
            a = a * a % q;
            k >>= 1;
        }

        return res;
    }
}

超大nm:III

import java.util.*;

public class Main {

    static int n, p;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t -- > 0) {

            long a = sc.nextLong(), b = sc.nextLong();
            p = sc.nextInt();

            long res = lucas(a, b);

            System.out.println(res);
        }
    }

    static long lucas(long a, long b) {
        if (a < p && b < p) return C(a, b);
        return C(a % p, b % p) * lucas(a / p, b / p) % p;
    }

    static long C(long a, long b) {
        if (a == b || b == 0) return 1;
        long res = 1;
        for (long i = 1, j = a; i <= b; i++, j--) {
            res = res * j % p;
            res = res * quickMi(i, p - 2) % p;
        }

        return res;
    }

    static long quickMi(long a, long k) {
        long res = 1;
        while (k != 0) {
            if ((k & 1) == 1) res = res * a % p;
            a = a * a % p;
            k >>= 1;
        }

        return res;
    }
}

无模数
直接使用高精度或者BigInteger