HDU 3903 Trigonometric Function

Problem Description

Give you a triangle ABC. Get more information in the picture below.



Now, give you 6 integers a, b, c, n, m and k. a, b and c are triangle ABC`s three edges. Can you judge whether the result of the following fraction is rational number? 



 

Input

There are several test cases in the input data.

Each case is just one line with 6 integers -- a, b, c, n, m, k (0< a, b, c, n, m, k < 10^4) separated by spaces. The input data ensures that sin(kC) will not be equal with 0.

 

Output

Each case output “YES”, if the result of the fraction is rational number, otherwise “NO”.

 

Sample Input

2
1 1 1 1 1 1
3 4 5 6 7 7

 

Sample Output

NO
YES
数学题，有结论的，如果cos A是有理数，那么cos nA也是，对于原式，分子一定是有理数，只要验证分母也是就行了。

#include<cstdio>
#include<string>
#include<cstring>
#include<vector>
#include<iostream>
#include<queue>
#include<cmath>
#include<bitset>
#include<algorithm>
using namespace std;
typedef long long LL;
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int maxn = 3e5 + 10;
int a, b, c, n, m, k, T;

int main()
{
scanf("%d", &T);
while (T--)
{
scanf("%d%d%d%d%d%d", &a, &b, &c, &n, &m, &k);
LL k = (LL)4 * a*a*b*b - (LL)(a*a + b*b - c*c)*(a*a + b*b - c*c);
LL sqr = sqrt(1.0*k);
if (sqr*sqr == k) printf("YES\n"); else printf("NO\n");
}
return 0;
}