Euler theorem（HDU 6124）

Euler theorem

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 524288/524288 K (Java/Others)

Total Submission(s): 494    Accepted Submission(s): 400

Problem Description

HazelFan is given two positive integers a,b， and he wants to calculate amodb. But now he forgets the value of b and only remember the value of a, please tell him the number of different possible results.

 

Input

The first line contains a positive integer T(1≤T≤5), denoting the number of test cases.
For each test case:
A single line contains a positive integer a(1≤a≤109).

 

Output

For each test case:
A single line contains a nonnegative integer, denoting the answer.

 

Sample Input

2
1
3

 

Sample Output

2
3

 //题意：给定正整数$a$，求对于所有正整数$b$，a\mod bamodb有多少种可能的结果。

//思路：显然小于<a/2的每个非负整数c都是可能成为余数的，取b=a-c即可，另外a本身也能成为余数，而其他数显然都不可能。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <string>
using namespace std;

int main()
{
	int T;
	scanf("%d", &T);
	while (T--)
	{
		int a;
		scanf("%d", &a);
		int ans = (a + 1) / 2 + 1;
		printf("%d\n", ans);
	}
	return 0;
}