Takahashi and Aoki will play a game. They will repeatedly play it until one of them have N wins in total.

When they play the game once, Takahashi wins with probability A %, Aoki wins with probability B %, and the game ends in a draw (that is, nobody wins) with probability C %. Find the expected number of games that will be played, and print it as follows.

We can represent the expected value as P/Q with coprime integers P and Q. Print the integer R between 0 and 10^9+6 (inclusive) such that R \times Q \equiv P\pmod {10^9+7}. (Such an integer R always uniquely exists under the constraints of this problem.)

Constraints

* 1 \leq N \leq 100000
* 0 \leq A,B,C \leq 100
* 1 \leq A+B
* A+B+C=100
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N A B C


Output

Print the expected number of games that will be played, in the manner specified in the statement.

Examples

Input

1 25 25 50


Output

2


Input

4 50 50 0


Output

312500008


Input

1 100 0 0


Output

1


Input

100000 31 41 28


Output

104136146
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    long long N, A, B, C;
    cin>>N>>A>>B>>C;

    long long M = 1000000007;

    auto powmod = [&](long long a, long long b)
    {
        long long r = 1;
        for (; b>0; b>>=1, a=a*a%M)
            if (b&1)
                r = r*a%M;
        return r;
    };

    auto inv = [&](long long a)
    {
        return powmod(a, M-2);
    };

    vector<long long> F(2*N);
    F[0] = 1;
    for (long long i=1; i<2*N; i++)
        F[i] = i*F[i-1]%M;

    long long ans = 0;
    for (long long i=N; i<=2*N-1; i++)
    {
        long long a = i*100;
        a *= inv(100-C);
        a %= M;
        a *= (powmod(A, N)*powmod(B, i-N) + powmod(A, i-N)*powmod(B, N)) % M;
        a %= M;
        a *= inv(powmod(A+B, i));
        a %= M;
        a *= F[i-1];
        a %= M;
        a *= inv(F[N-1])*inv(F[i-N])%M;
        a %= M;
        ans += a;
        ans %= M;
    }
    cout<<ans<<endl;
}
