Key Set
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others) Total Submission(s): 2244 Accepted Submission(s): 1172
Problem Description
soda has a set
S
with
n
integers
{1,2,…,n}
. A set is called key set if the sum of integers in the set is an even number. He wants to know how many nonempty subsets of
S
are key set.
Input
There are multiple test cases. The first line of input contains an integer
T
(1≤T≤105)
, indicating the number of test cases. For each test case:
The first line contains an integer
n
(1≤n≤109)
, the number of integers in the set.
Output
For each test case, output the number of key sets modulo 1000000007.
Sample Input
4
1
2
3
4
Sample Output
0
1
3
7
题解：快速幂算法的应用；
代码如下：
#include<cstdio>
#include<cmath>
typedef long long ll;
ll mod_pow(ll x,ll n,ll mod){
ll res=1;
while(n>0){
if(n&1) res=res*x%mod;
x=x*x%mod;
n>>=1;
}
return res;
}
int main()
{
int t;
scanf("%d",&t);
while(t--){
ll n;
scanf("%lld",&n);
printf("%lld\n",mod_pow(2,n-1, 1000000007)-1);
}
return 0;
}
