Loj 6165. A water problem (linear sieve)

Title Description Transmission Door

The main idea is to find the smallest integer that can divide [1,n] into 100000007. Solving

is actually to ask for the least common multiple in [1,n], least common multiple equals ∏pimax (QI) \prod Pi^{max (QI)}
That is, the product of the maximum power of all the mass factors.
Just beginning to think that the 108 10^8 linear sieve can not be, but the loj of the evaluation machine is faster, all directly do the code

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define N 100000003
#define MX 10000
#define LL long long 
#define P 100000007
using namespace std;
bool Pd[n];
int n,prime[6000000];
int main ()
{
    scanf ("%d", &n); LL Ans=1;
    for (int i=2;i<=n;i++) {
        if (!pd[i]) {
            prime[++prime[0]]=i;
            LL t=i;
            while (t* (LL) i<=n) t*=i;
            ans=ans*t%p;
        }
        for (int j=1;j<=prime[0];j++) {
            int k=i*prime[j];
            if (k>n) break;
            Pd[k]=1;
            if (i%prime[j]==0) break;
        }
    }
    printf ("%lld\n", ans);
}