SGU247(排列组合与大数运算)

题目：Difficult Choice

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题目分析以及公式推导：

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import java.io.*;
import java.util.*;
import java.math.BigInteger;

public class Solution
{
	 public static BigInteger fac[]=new BigInteger[2013];
	 public static void main(String[] args)
	 {
		  init();
		  Scanner cin = new Scanner(System.in);
		  int t = cin.nextInt();
		  while(t--!=0)
		  {
			   int p=cin.nextInt();
			   BigInteger ans=fac[2*p];
			   BigInteger temp=fac[p];
			   ans=ans.divide(temp);
			   ans=ans.divide(temp);
			   ans=ans.subtract(BigInteger.valueOf(2));
			   ans=ans.divide(BigInteger.valueOf(p));
			   ans=ans.add(BigInteger.valueOf(2));
			   System.out.println(ans);
		  }
	 }
	 public static void init()
	 {
		  for(int i=1;i<2012;i++)
			  fac[i]=BigInteger.ONE;
		  for(int i=2;i<2012;i++)
			  fac[i]=fac[i-1].multiply(BigInteger.valueOf(i));
	 }
}