設50元的人為+1 100元的人為-1 滿足前隨意k個人的和大於等於0 卡特蘭數

C(n+m, m)-C(n+m, m+1)*n!*m!

import java.math.*;
import java.util.*;


public class Main {

    /**
     * @param args
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int cas = 1;
        while(true){
            int m = sc.nextInt();
            int n = sc.nextInt();
            if(m == 0 && n == 0)
                break;
            System.out.println("Test #"+cas+":");
            cas++;
            if(m < n){
                System.out.println(0);
                continue;
            }
            BigInteger ans1 = BigInteger.valueOf(1);
            int x = n+m;
            for(int i = 1; i <= m; i++){
                ans1 = ans1.multiply(BigInteger.valueOf(x));
                x--;
            }
            for(int i = 1; i <= n; i++){
                ans1 = ans1.multiply(BigInteger.valueOf(i));
            }
            BigInteger ans2 = BigInteger.valueOf(1);
            x = n+m;
            for(int i = 1; i <= m+1; i++){
                ans2 = ans2.multiply(BigInteger.valueOf(x));
                x--;
                ans2 = ans2.divide(BigInteger.valueOf(i));
            }
            for(int i = 1; i <= n; i++){
                ans2 = ans2.multiply(BigInteger.valueOf(i));
            }
            for(int i = 1; i <= m; i++){
                ans2 = ans2.multiply(BigInteger.valueOf(i));
            }
            
            System.out.println(ans1.subtract(ans2));
        }
    }
}

HDU 1133 Buy the Ticket 卡特蘭數