Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

1 25 25 50

Sample Output 1

2

Since N=1, they will repeat the game until one of them wins.
The expected number of games played is 2.

Sample Input 2

4 50 50 0

Sample Output 2

312500008

C may be 0.

Sample Input 3

1 100 0 0

Sample Output 3

1

B may also be 0.

Sample Input 4

100000 31 41 28

Sample Output 4

104136146

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CBestOf2n1 solver = new CBestOf2n1();
        solver.solve(1, in, out);
        out.close();
    }

    static class CBestOf2n1 {
        static final int mod = (int) 1e9 + 7;

        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();

//        a = b = 1;

//        for (int i = 0; i < 200; i++) {
//            dump(i, 312500008L * i % mod);
//        }

            long sum = 0;
            Combination comb = new Combination(2 * n + 10, mod);
            long p = 0;
            for (int i = 0; i < n; i++) {
                long v = (powmod(a, n, mod) * powmod(b, i, mod) % mod + powmod(b, n, mod) * powmod(a, i, mod) % mod) % mod;
                long pp = comb.get(n - 1 + i, n - 1) * v % mod;
                sum = sum % mod * (a + b) % mod;
                sum += pp;
                p = p % mod * (a + b) % mod;
                p += pp % mod * (n + i) % mod;
            }
//        for (int i = 0; i < n; i++) {
//            p = p * (a + b) % mod;
//            long v = (powmod(a, n, mod) * powmod(b, i, mod) % mod + powmod(b, n, mod) * powmod(a, i, mod) % mod) % mod;
//            long pp = comb.get(n + i, n) * v % mod;
//            p += sum * pp % mod * (n + i) % mod;
//        }
            p %= mod;
            sum %= mod;
            dump(p);
            p = p % mod * 100 % mod;
            p = p * powmod(100 - c, mod - 2, mod) % mod;
//        dump(p, powmod(a + b, 2 * n - 1, mod));
            dump(p, sum);
//        sum = sum * powmod(powmod(a + b, 2 * n - 1, mod), mod - 2, mod) % mod;
            p = p * powmod(sum, mod - 2, mod) % mod;
            out.println(p);
        }

        static long powmod(long n, long r, int m) {
            long res = 1;
            for (; r != 0; r >>>= 1, n = n * n % m) {
                if ((r & 1) == 1) {
                    res = res * n;
                    if (res >= m) {
                        res %= m;
                    }
                }
            }
            return res;
        }

        static void dump(Object... o) {
            System.err.println(Arrays.deepToString(o));
        }

        public class Combination {
            final int mod;
            final int MAX;
            final long[] fact;
            final long[] inv;
            final long[] invfact;

            public Combination(int n, int mod) {
                this.mod = mod;
                MAX = n + 1;
                fact = new long[MAX];
                invfact = new long[MAX];
                inv = new long[MAX];

                inv[1] = 1;
                for (int i = 2; i < inv.length; i++) {
                    inv[i] = inv[mod % i] * (mod - mod / i) % mod;
                }

                fact[0] = 1;
                invfact[0] = 1;
                for (int i = 1; i < inv.length; i++) {
                    fact[i] = i * fact[i - 1] % mod;
                    invfact[i] = inv[i] * invfact[i - 1] % mod;
                }
            }

            public long get(int n, int r) {
                return fact[n] * invfact[n - r] % mod * invfact[r] % mod;
            }

        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}