Problem: You are given an integer sequence of length N: A_1,A_2,...,A_N. Let us perform Q operations in order. The i-th operation is described by two integers X_i and Y_i. In this operation, we will choose one of the following two actions and perform it:

* Swap the values of A_{X_i} and A_{Y_i}
* Do nothing



There are 2^Q ways to perform these operations. Find the sum of the inversion numbers of the final sequences for all of these ways to perform operations, modulo 10^9+7.

Here, the inversion number of a sequence P_1,P_2,...,P_M is the number of pairs of integers (i,j) such that 1\leq i < j\leq M and P_i > P_j.

Constraints

* 1 \leq N \leq 3000
* 0 \leq Q \leq 3000
* 0 \leq A_i \leq 10^9(1\leq i\leq N)
* 1 \leq X_i,Y_i \leq N(1\leq i\leq Q)
* X_i\neq Y_i(1\leq i\leq Q)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N Q
A_1
:
A_N
X_1 Y_1
:
X_Q Y_Q


Output

Print the sum of the inversion numbers of the final sequences, modulo 10^9+7.

Examples

Input

3 2
1
2
3
1 2
1 3


Output

6


Input

5 3
3
2
3
1
4
1 5
2 3
4 2


Output

36


Input

9 5
3
1
4
1
5
9
2
6
5
3 5
8 9
7 9
3 2
3 8


Output

425

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 {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int q = in.readInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.readInt();
            }
            int[][] swaps = new int[q][2];
            for (int i = 0; i < q; i++) {
                swaps[i][0] = in.readInt() - 1;
                swaps[i][1] = in.readInt() - 1;
            }



            NumberTheory.Modular mod = new NumberTheory.Modular(1e9 + 7);
            NumberTheory.Power pow = new NumberTheory.Power(mod);
            int inv2 = pow.inverse(2);

            int[][] dp = new int[n][n];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (a[i] < a[j]) {
                        dp[i][j]++;
                    }
                }
            }

            int[] xInL = new int[n];
            int[] xInR = new int[n];

            for (int j = 0; j < q; j++) {
                int x = swaps[j][0];
                int y = swaps[j][1];

                // x in l
                for (int r = 0; r < n; r++) {
                    if (r == y || r == x) {
                        xInL[r] = 0;
                        continue;
                    }
                    xInL[r] = mod.plus(dp[y][r], dp[x][r]);
                }


                // x in r
                for (int l = 0; l < n; l++) {
                    if (l == y || l == x) {
                        xInR[l] = 0;
                        continue;
                    }
                    xInR[l] = mod.plus(dp[l][x], dp[l][y]);
                }

                int xy = dp[x][y];
                int yx = dp[y][x];

                // update x in l
                for (int i = 0; i < n; i++) {
                    int half = mod.mul(inv2, xInL[i]);
                    dp[x][i] = dp[y][i] = half;
                }

                // update x in r
                for (int i = 0; i < n; i++) {
                    int half = mod.mul(inv2, xInR[i]);
                    dp[i][x] = dp[i][y] = half;
                }

                int half = mod.mul(mod.plus(xy, yx), inv2);
                dp[x][y] = dp[y][x] = half;
            }

            int p = pow.pow(2, q);
            int ans = 0;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (i > j) {
                        ans = mod.plus(dp[i][j], ans);
                    }
                }
            }
            ans = mod.mul(p, ans);


            out.println(ans);
        }

    }
    static class NumberTheory {
        public static class Modular {
            int 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;
            }

        }

        public static class Power {
            final NumberTheory.Modular modular;

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

            public int pow(int x, long 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;
            }

            public int inverse(int x) {
                return pow(x, modular.m - 2);
            }

        }

    }
    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 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();
        }

    }
}