Codeforces 385 C. Bear and Prime Numbers

把求和混到求素数里就快多了。。。。

C. Bear and Prime Numbers

time limit per test

2 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

Recently, the bear started studying data structures and faced the following problem.

You are given a sequence of integers x1, x2, ..., xn of length n and m queries, each of them is characterized by two integers li, ri. Let's introduce f(p) to represent the number of such indexes k, that xk is divisible by p. The answer to the query li, ri is the sum: , where S(li, ri) is a set of prime numbers from segment [li, ri] (both borders are included in the segment).

Help the bear cope with the problem.

Input

The first line contains integer n (1 ≤ n ≤ 106). The second line contains n integers x1, x2, ..., xn (2 ≤ xi ≤ 107). The numbers are not necessarily distinct.

The third line contains integer m (1 ≤ m ≤ 50000). Each of the following m lines contains a pair of space-separated integers, li and ri(2 ≤ li ≤ ri ≤ 2·109) — the numbers that characterize the current query.

Output

Print m integers — the answers to the queries on the order the queries appear in the input.

Sample test(s)

input

65 5 7 10 14 1532 113 124 4

output

970

input

72 3 5 7 11 4 828 102 123

output

07

Note

Consider the first sample. Overall, the first sample has 3 queries.

1. The first query l = 2, r = 11 comes. You need to count f(2) + f(3) + f(5) + f(7) + f(11) = 2 + 1 + 4 + 2 + 0 = 9.
2. The second query comes l = 3, r = 12. You need to count f(3) + f(5) + f(7) + f(11) = 1 + 4 + 2 + 0 = 7.
3. The third query comes l = 4, r = 4. As this interval has no prime numbers, then the sum equals 0.

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int maxn=10000010;int ct[maxn],vis[maxn];bool pr[maxn];void getprime(){    memset(pr,true,sizeof(pr));    pr[0]=pr[1]=0;    for(int i=2;i<maxn;i++)    {        if(pr[i])        {            if(vis[i]) ct[i]+=vis[i];            for(int j=i*2;j<maxn;j+=i)            {                if(vis[j]) ct[i]+=vis[j];                pr[j]=false;            }        }    }    for(int i=2;i<maxn;i++)    {        ct[i]+=ct[i-1];    }}int n,m;int main(){    scanf("%d",&n);    int maxd=0;    for(int i=0;i<n;i++)    {        int a;        scanf("%d",&a);        vis[a]++;    }    getprime();    scanf("%d",&m);    while(m--)    {        int l,r;        scanf("%d%d",&l,&r);        if(l>maxn) l=maxn-1;        if(r>maxn) r=maxn-1;        printf("%d\n",ct[r]-ct[l-1]);    }    return 0;}