K Simple question （第十届山东理工大学ACM网络编程擂台赛 正式赛）

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <assert.h>

const int maxn = 110000005;
const int mod = 100000007;
const int N = 60000008;
int prime[N];
bool vis[maxn];
int main()
{
    int n;
    while(~scanf("%d",&n)){
    assert(1 <= n && n <= 100000000);
    long long ans = 1;
    int cnt=0;
    memset(vis,false, sizeof(vis));
    for (int i = 2; i <= n; i++)
    {
        if (!vis[i])
        {
            prime[cnt++] = i;
            for (long long j = i; j <= n; j *= i)
            {
                ans = ans * i % mod;
            }
        }
        for (int j = 0; j < cnt; j++)
        {
            long long x = i * prime[j];
            if (x > n)break;
            vis[x] = true;
            if (i%prime[j] == 0)break;
        }
    }
    printf("%lld\n",ans);
    }
return 0;
}