factorial vs pow 더블릿 (PS)

#include <stdio.h>
#include <cmath>
 
using namespace std;
 
double fac[10000000] = { 0 };
 
void solve(int num) {    
    int left = 0, right = 10000000,rst=0;
    while (left <= right) {        
        int mid = (left + right) / 2;
        double pow = mid*log10(num);
 
        if (pow >= fac[mid]) {
            left = mid + 1;
        }
        else{
            rst = mid;
            right = mid - 1;
        }
    }
    printf("%d\n", rst);
}
 
int main() {
    for (int i = 1; i < 10000000; i++) {
        fac[i] = fac[i - 1] + log10(i);        
    }    
 
    int t;
    scanf("%d", &t);
    getchar();
 
    while (t--) {
        int n;
        scanf("%d", &n);
        solve(n);        
    }
}