Language: C++

#define _GLIBCXX_DEBUG//TLEの原因になるので注意！！！！！！！！！！！
#include<cmath>
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
vector<ll> arr;
stack<int> st;
queue<int> qu;
queue<pair<int,int> > qu2;
priority_queue<int> pq;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
#define rep2(i,n) for(int i=1; i<=(int)(n); i++)
#define mins(x,y) x=min(x,y)
#define maxs(x,y) x=max(x,y)
typedef set<int> set_t;
typedef set<string> set_g;
typedef complex<double> xy_t;
static const int NIL = -1;
static const int INF = 1000000007;
#define mp make_pair
#define sz(x) int(x.xise())
#define mod 1000000007
#define reps(i,s,n) for(int i = s; i < n; i++)
deque<int> deq;
//#define int long long

//cerrはコメントアウトしなくても通る//ただしTLEを引き起こすことがある

ll f[100005];
//int n,k とかしておく

ll pw(ll x, ll y){//euclidの互除法より
    ll a= 1;
    while(y){
        if(y&1){//奇数なら
            a = a*x%mod;
        }
        x = x*x%mod;
        y /= 2;
    }
    return a;
}

ll modinv(ll x){//逆元を求める
    return pw(x, mod - 2 );
}

ll comb(ll n,ll r){
    if(n<r){
        return 0;
    }
    //cerr<<f[n]<<' '<<modinv(f[r])<<' '<<modinv(f[n-r])<<endl;
    //cerr<<n-r<<endl;
    return f[n] * modinv(f[r])%mod*modinv(f[n-r])%mod;
    //cerr<<f[n]<<' '<<modinv(f[r])<<' '<<modinv(f[n-r])<<endl;
}//対combination//ただしfは用意してね

/*
    f[0]=1;
    rep2(i,200005){
        f[i]=f[i-1]*i;
        f[i]%=mod;
    }
*/


ll hcomb(ll n,ll r){   
    if(n==0){
        return 0;
    } 
    if(r==1){
        return comb(n,r);
    }
    return comb(n+r-1,r-1);
}

ll g[1000000007];

int main(){
    f[0]=1;
    rep2(i,100000){
        f[i]=f[i-1]*i;
        f[i]%=mod;
        /*
        if(i<10){
            //cerr<<f[i]<<endl;
        }
        */
    }

    int n,m;

    cin >> n>>m;
    //int s=0;
    for(int i=2;i<100007;){
        while(m%i==0){
            g[i]++;
            m/=i;
            //s++;
        }
        if(g[i]>0){
            arr.push_back(g[i]);
            cerr<<g[i]<<endl;
        }
        if(i==2){
            i+=1;
        }else{
            i+=2;
        }
    }
    ll ans=1;
    //cerr<<s<<' '<<n<<' '<<ans<<endl;
    rep(i,arr.size()){
        ans*=hcomb(arr[i],n);
        ans%=mod;
    }
    cout<<ans<<endl;
    return 0;
}

Compiler output:
/tmp/ccP6H5nW.o: in function `__gnu_debug::_Error_formatter::_S_at(char const*, unsigned int, char const*)':
a.cc:(.text._ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_[_ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_]+0x16): relocation truncated to fit: R_X86_64_PC32 against symbol `guard variable for __gnu_debug::_Error_formatter::_S_at(char const*, unsigned int, char const*)::__formatter' defined in .bss._ZGVZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter[_ZGVZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter] section in /tmp/ccP6H5nW.o
a.cc:(.text._ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_[_ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_]+0x26): relocation truncated to fit: R_X86_64_PC32 against symbol `guard variable for __gnu_debug::_Error_formatter::_S_at(char const*, unsigned int, char const*)::__formatter' defined in .bss._ZGVZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter[_ZGVZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter] section in /tmp/ccP6H5nW.o
a.cc:(.text._ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_[_ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_]+0x4c): relocation truncated to fit: R_X86_64_PC32 against symbol `__gnu_debug::_Error_formatter::_S_at(char const*, unsigned int, char const*)::__formatter' defined in .bss._ZZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter[_ZZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter] section in /tmp/ccP6H5nW.o
a.cc:(.text._ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_[_ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_]+0x5b): relocation truncated to fit: R_X86_64_PC32 against symbol `guard variable for __gnu_debug::_Error_formatter::_S_at(char const*, unsigned int, char const*)::__formatter' defined in .bss._ZGVZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter[_ZGVZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter] section in /tmp/ccP6H5nW.o
a.cc:(.text._ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_[_ZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_]+0x6a): relocation truncated to fit: R_X86_64_PC32 against symbol `__gnu_debug::_Error_formatter::_S_at(char const*, unsigned int, char const*)::__formatter' defined in .bss._ZZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter[_ZZN11__gnu_debug16_Error_formatter5_S_atEPKcjS2_E11__formatter] section in /tmp/ccP6H5nW.o
collect2: error: ld returned 1 exit status