Problem: Once, during a lesson, Sasha got bored and decided to talk with his friends. Suddenly, he saw Kefa. Since we can talk endlessly about Kefa, we won't even start doing that. The conversation turned to graphs. Kefa promised Sasha to tell him about one interesting fact from graph theory if Sasha helps Kefa to count the number of beautiful trees. 

In this task, a tree is a weighted connected graph, consisting of n vertices and n-1 edges, and weights of edges are integers from 1 to m. Kefa determines the beauty of a tree as follows: he finds in the tree his two favorite vertices — vertices with numbers a and b, and counts the distance between them. The distance between two vertices x and y is the sum of weights of edges on the simple path from x to y. If the distance between two vertices a and b is equal to m, then the tree is beautiful.

Sasha likes graph theory, and even more, Sasha likes interesting facts, that's why he agreed to help Kefa. Luckily, Sasha is familiar with you the best programmer in Byteland. Help Sasha to count the number of beautiful trees for Kefa. Two trees are considered to be distinct if there is an edge that occurs in one of them and doesn't occur in the other one. Edge's weight matters.

Kefa warned Sasha, that there can be too many beautiful trees, so it will be enough to count the number modulo 10^9 + 7.

Input

The first line contains four integers n, m, a, b (2 ≤ n ≤ 10^6, 1 ≤ m ≤ 10^6, 1 ≤ a, b ≤ n, a ≠ b) — the number of vertices in the tree, the maximum weight of an edge and two Kefa's favorite vertices.

Output

Print one integer — the number of beautiful trees modulo 10^9+7.

Examples

Input


3 2 1 3


Output


5


Input


3 1 1 2


Output


2


Input


5 15 1 5


Output


345444

Note

There are 5 beautiful trees in the first example:

<image>

In the second example the following trees are beautiful:

<image>

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            TaskD solver = new TaskD();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class TaskD {
        Modular mod = new Modular(1e9 + 7);
        Power power = new Power(mod);
        InverseNumber inverseNumber = new InverseNumber(1000000, mod);
        Factorial factorial = new Factorial(1000000, mod);
        Composite comp = new Composite(factorial);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int m = in.readInt();
            int a = in.readInt();
            int b = in.readInt();

            CachedPow cachedPow = new CachedPow(m, n, mod);
            int ans = 0;
            for (int i = 0; i <= n - 2; i++) {
                int local = comp.composite(n - 2, i);
                local = mod.mul(local, factorial.fact(i));
                int total = i + 1;
                local = mod.mul(local, comp.composite((m - total) + total - 1, total - 1));
                local = mod.mul(local, cachedPow.pow(n - 1 - total));
                local = mod.mul(local, countTree(n - 2 - i + 1, 2 + i));
                ans = mod.plus(ans, local);
            }

            out.println(ans);
        }

        public int countTree(int n, int x) {
            if (n == 1) {
                return 1;
            }
            int p1 = x;
            int p2 = power.pow(n - 1, n - 2);
            int p3 = mod.plus(1, mod.mul(x, inverseNumber.inverse(n - 1)));
            p3 = power.pow(p3, n - 2);
            return mod.mul(p1, mod.mul(p2, p3));
        }

    }

    static class Composite {
        final Factorial factorial;
        final Modular modular;

        public Composite(Factorial factorial) {
            this.factorial = factorial;
            this.modular = factorial.getModular();
        }

        public Composite(int limit, Modular modular) {
            this(new Factorial(limit, modular));
        }

        public int composite(int m, int n) {
            if (n > m) {
                return 0;
            }
            return modular.mul(modular.mul(factorial.fact(m), factorial.invFact(n)), factorial.invFact(m - n));
        }

    }

    static class CachedPow {
        private int[] first;
        private int[] second;
        private Modular mod;

        public CachedPow(int x, int maxExp, Modular mod) {
            this.mod = mod;
            int k = Math.max(1, (int) DigitUtils.round(Math.sqrt(maxExp)));
            first = new int[k];
            second = new int[maxExp / k + 1];
            first[0] = 1;
            for (int i = 1; i < k; i++) {
                first[i] = mod.mul(x, first[i - 1]);
            }
            second[0] = 1;
            int step = mod.mul(x, first[k - 1]);
            for (int i = 1; i < second.length; i++) {
                second[i] = mod.mul(second[i - 1], step);
            }
        }

        public int pow(int exp) {
            return mod.mul(first[exp % first.length], second[exp / first.length]);
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class InverseNumber {
        int[] inv;

        public InverseNumber(int[] inv, int limit, Modular modular) {
            this.inv = inv;
            inv[1] = 1;
            int p = modular.getMod();
            for (int i = 2; i <= limit; i++) {
                int k = p / i;
                int r = p % i;
                inv[i] = modular.mul(-k, inv[r]);
            }
        }

        public InverseNumber(int limit, Modular modular) {
            this(new int[limit + 1], limit, modular);
        }

        public int inverse(int x) {
            return inv[x];
        }

    }

    static class Factorial {
        int[] fact;
        int[] inv;
        Modular modular;

        public Modular getModular() {
            return modular;
        }

        public Factorial(int[] fact, int[] inv, InverseNumber in, int limit, Modular modular) {
            this.modular = modular;
            this.fact = fact;
            this.inv = inv;
            fact[0] = inv[0] = 1;
            for (int i = 1; i <= limit; i++) {
                fact[i] = modular.mul(fact[i - 1], i);
                inv[i] = modular.mul(inv[i - 1], in.inv[i]);
            }
        }

        public Factorial(int limit, Modular modular) {
            this(new int[limit + 1], new int[limit + 1], new InverseNumber(limit, modular), limit, modular);
        }

        public int fact(int n) {
            return fact[n];
        }

        public int invFact(int n) {
            return inv[n];
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static long round(double x) {
            if (x >= 0) {
                return (long) (x + 0.5);
            } else {
                return (long) (x - 0.5);
            }
        }

    }

    static class Power {
        final Modular modular;

        public Power(Modular modular) {
            this.modular = modular;
        }

        public int pow(int x, int n) {
            if (n == 0) {
                return modular.valueOf(1);
            }
            long r = pow(x, n >> 1);
            r = modular.valueOf(r * r);
            if ((n & 1) == 1) {
                r = modular.valueOf(r * x);
            }
            return (int) r;
        }

    }

    static class Modular {
        int m;

        public int getMod() {
            return m;
        }

        public Modular(int m) {
            this.m = m;
        }

        public Modular(long m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public Modular(double m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public String toString() {
            return "mod " + m;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput println(int c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}