Prime Number CodeForces - 359C (属于是数论)
Simon has a prime number x and an array of non-negative integers a1, a2, ..., an.
Simon loves fractions very much. Today he wrote out number on
a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction:
,
where number t equals xa1 + a2 + ... + an.
Now Simon wants to reduce the resulting fraction.
Help him, find the greatest common divisor of numbers s and t. As GCD can be rather large, print it as a remainder after dividing it by number 1000000007 (109 + 7).
The first line contains two positive integers n and x (1 ≤ n ≤ 105, 2 ≤ x ≤ 109) — the size of the array and the prime number.
The second line contains n space-separated integers a1, a2, ..., an (0 ≤ a1 ≤ a2 ≤ ... ≤ an ≤ 109).
Print a single number — the answer to the problem modulo 1000000007 (109 + 7).
2 2 2 2
8
3 3 1 2 3
27
2 2 29 29
73741817
4 5 0 0 0 0
1
In the first sample . Thus, the answer to the problem is 8.
In the second sample, . The answer to the problem is 27,
as351 = 13·27, 729 = 27·27.
In the third sample the answer to the problem is 1073741824 mod 1000000007 = 73741817.
In the fourth sample . Thus, the answer to the problem is 1.
#include<queue> #include<stack> #include<vector> #include<math.h> #include<stdio.h> #include<numeric>//STL数值算法头文件 #include<stdlib.h> #include<string.h> #include<iostream> #include<algorithm> #include<functional>//模板类头文件 using namespace std; const long long INF=1e9+7; const long long maxn=101000; long long n,x; long long a[maxn]; long long quick_mod(long long a,long long b) { long long ans=1; a=a%INF; while(b) { if(b&1) ans=ans*a%INF; a=a*a%INF; b>>=1; } return ans; } int main() { while(~scanf("%d %d",&n,&x)) { long long sum1=0; for(long long i=0; i<n; i++) { scanf("%d",&a[i]); sum1+=a[i]; } for(long long i=0; i<n; i++) a[i]=sum1-a[i]; sort(a,a+n); long long ans,j=1,cot=1,t; for(j=1; j<=n; j++) { if(a[j]!=a[j-1]) { if(cot%x) { ans=a[j-1]; break; } else { cot/=x; a[j-1]+=1; j--; } } else cot++; } printf("%d\n",quick_mod(x,min(ans,sum1))); } return 0; } #include<queue> #include<stack> #include<vector> #include<math.h> #include<stdio.h> #include<numeric>//STL数值算法头文件 #include<stdlib.h> #include<string.h> #include<iostream> #include<algorithm> #include<functional>//模板类头文件 using namespace std; const long long INF=1e9+7; const long long maxn=101000; long long n,x; long long a[maxn]; long long gcd(long long a,long long b) { long long ans=1; ans=ans%INF; while(b) { if(b&1) ans=ans*a%INF; a=a*a%INF; b>>=1; } return ans; } int main() { while(~scanf("%I64d %I64d",&n,&x)) { long long sum1=0; for(long long i=0; i<n; i++) { scanf("%I64d",&a[i]); sum1+=a[i]; } for(long long i=0; i<n; i++) a[i]=sum1-a[i]; sort(a,a+n); long long ans,j=1,cot=1,t; while(j<=n) { if(a[j]!=a[j-1]) { if(cot%x) { ans=a[j-1]; break; } long long f=a[j-1]+1; t=cot/x; for(long long k=j-1,s=t; s>0; s--,k--) a[k]=f; j-=t; j++; cot=1; } else cot++,j++; } printf("%I64d\n",gcd(x,min(ans,sum1))); } return 0; }