Mathematical knowledge: finding combinatorial number IV - finding combinatorial number

subject ：AcWing 888. Find the combination number IV
Input a,b, seek C^b_a Value .

Note that the results can be large , Need to use high-precision calculation .

Input format
All in one line , Contains two integers a and b.

Output format
All in one line , Output C^b_a Value .

Data range
1≤b≤a≤5000

sample input ：

5 3

sample output ：

10

Topic analysis ：
The steps of this problem ：
1. Screening primes
2. Find the number of times of each prime
3. Multiply all prime factors with high precision

#include <iostream>
#include <vector>

using namespace std;

const int N = 5010;
int primes[N],cnt;
int sum[N];
bool st[N];

void get_prime(int n) //  Screening primes 
{
    
    for(int i=2;i<=n;i++)
    {
    
        if(!st[i])primes[cnt++]=i;
        for(int j=0;primes[j]<=n/i;j++)
        {
    
            st[primes[j]*i]=true;
            if(i%primes[j]==0)break;
        }
    }
}

int get(int n,int p) //  Number of primes obtained 
{
    
    int res=0;
    while(n)
    {
    
        res+=n/p;
        n/=p;
    }
    return res;
}
// High precision multiplication 
vector<int> mul(vector<int> a,int b)
{
    
    vector<int> c;
    int t=0;
    for (int i=0;i<a.size();i++)
    {
    
        t+=a[i]*b;
        c.push_back(t%10);
        t/=10;
    }
    while(t)
    {
    
        c.push_back(t%10);
        t/=10;
    }
    return c;
}

int main()
{
    
    int a,b;
    cin>>a>>b;
    get_prime(a);
    
    for(int i=0;i<cnt;i++)
    {
    
        int p=primes[i];
        sum[i]=get(a,p)-get(a-b,p)-get(b,p);
    }
    
    vector<int> res;
    res.push_back(1);

    for(int i=0;i<cnt;i++)
        for(int j=0;j<sum[i];j++)
            res = mul(res, primes[i]);

    for(int i=res.size()-1;i>=0;i--)cout<<res[i];
    cout<<endl;

    return 0;
}