RXD and math
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 261 Accepted Submission(s): 134
Total Submission(s): 261 Accepted Submission(s): 134
Problem Description
RXD is a good mathematician.
One day he wants to calculate:
output the answer module 109+7.
1≤n,k≤1018
p1,p2,p3…pk are different prime numbers
One day he wants to calculate:
∑i=1nkμ2(i)×⌊nki−−−√⌋
output the answer module 109+7.
1≤n,k≤1018
μ(n)=1(n=1)
μ(n)=(−1)k(n=p1p2…pk)
μ(n)=0(otherwise)
p1,p2,p3…pk are different prime numbers
Input
There are several test cases, please keep reading until EOF.
There are exact 10000 cases.
For each test case, there are 2 numbers n,k.
There are exact 10000 cases.
For each test case, there are 2 numbers n,k.
Output
For each test case, output "Case #x: y", which means the test case number and the answer.
Sample Input
10 10
Sample Output
Case #1: 999999937
直接暴力打表,发现是n^k,快速幂直接水过
///AC代码
/* ***********************************************
┆ ┏┓ ┏┓ ┆
┆┏┛┻━━━┛┻┓ ┆
┆┃ ┃ ┆
┆┃ ━ ┃ ┆
┆┃ ┳┛ ┗┳ ┃ ┆
┆┃ ┃ ┆
┆┃ ┻ ┃ ┆
┆┗━┓ 马 ┏━┛ ┆
┆ ┃ 勒 ┃ ┆
┆ ┃ 戈 ┗━━━┓ ┆
┆ ┃ 壁 ┣┓┆
┆ ┃ 的草泥马 ┏┛┆
┆ ┗┓┓┏━┳┓┏┛ ┆
┆ ┃┫┫ ┃┫┫ ┆
┆ ┗┻┛ ┗┻┛ ┆
************************************************ */
#include <iostream>
#include <set>
#include <map>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <bitset>
#include <string>
#include <vector>
#include <iomanip>
#include <cstring>
#include <algorithm>
#include <functional>
#define PI acos(-1)
#define eps 1e-8
#define inf 0x3f3f3f3f
#define debug(x) cout<<"---"<<x<<"---"<<endl
typedef long long ll;
using namespace std;
const int mod = 1e9 + 7;
long long pow(long long a, long long n)
{
long long text = 1;
while (n)
{
if (n & 1)
{
text = (text % mod) * (a % mod) % mod;
}
a = (a % mod) * (a % mod) % mod;
n >>= 1;
}
return text;
}
int main()
{
long long n, k;
int i = 1;
while (~scanf("%lld%lld", &n, &k))
{
long long text = pow(n, k);
printf("Case #%d: %lld\n", i++, text);
}
return 0;
}
/************************************************
┆ ┏┓ ┏┓ ┆
┆┏┛┻━━━┛┻┓ ┆
┆┃ ┃ ┆
┆┃ ━ ┃ ┆
┆┃ ┳┛ ┗┳ ┃ ┆
┆┃ ┃ ┆
┆┃ ┻ ┃ ┆
┆┗━┓ ┏━┛ ┆
┆ ┃ ┃ ┆
┆ ┃ ┗━━━┓ ┆
┆ ┃ AC代马 ┣┓┆
┆ ┃ ┏┛┆
┆ ┗┓┓┏━┳┓┏┛ ┆
┆ ┃┫┫ ┃┫┫ ┆
┆ ┗┻┛ ┗┻┛ ┆
************************************************ */