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
import java.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		prepareFact();

		int need = sc.nextInt();
		int winT = sc.nextInt();
		int winA = sc.nextInt();
		int draw = sc.nextInt();
		long ans = 0;
		for(int m = need; m < need * 2; m ++) {
			long drawVal = mod(m * 100 * invMod(100 - draw));
			long combi = combiMod(m - 1, need - 1);
			long winTs = mod(powerMod(winT, need) * powerMod(winA, m - need));
			long winAs = mod(powerMod(winA, need) * powerMod(winT, m - need));
			long wins = mod(mod(winTs + winAs) * invMod(powerMod(winT + winA, m)));
			long tmp = mod(mod(wins * combi) * drawVal);
			ans = mod(ans + tmp);
		}
		System.out.println(ans);
	}

	static long MOD = (long)Math.pow(10, 9) + 7;
	public static long mod(long i) {
		return i % MOD + ((i % MOD) < 0 ? MOD : 0);
	}
	
	static long powerMod(long x, long y) {
		if (y == 0) {
			return 1;
		} else if (y == 1) {
			return x;
		} else if (y % 2 == 0) {
			long tmp = powerMod(x, y / 2);
			return mod(tmp * tmp);
		} else {
			long tmp = powerMod(x, y / 2);
			return mod(mod(tmp * tmp) * x);
		}
	}
	
	static long invMod(long x) {
		return powerMod(x, MOD - 2);
	}
	
	static int MAX_FACT = 200_100;
	static long factMod[] = new long[MAX_FACT];
	static void prepareFact() {
		factMod[0] = 1;
		for(int i = 1; i < MAX_FACT; i ++) {
			factMod[i] = mod(factMod[i - 1] * i);
		}
	}

	static long combiMod(int n, int r) {
		if(n < 0 || n < r) { return 0; }
		if(r == 0 || r == n) { return 1; }
		return mod(mod(factMod[n] * invMod(factMod[r])) * invMod(factMod[n - r]));
	}
}