Problem: Ron is a happy owner of a permutation a of length n.

A permutation of length n is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

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Ron's permutation is subjected to m experiments of the following type: (r_i, p_i). This means that elements in range [1, r_i] (in other words, the prefix of length r_i) have to be sorted in ascending order with the probability of p_i. All experiments are performed in the same order in which they are specified in the input data.

As an example, let's take a look at a permutation [4, 2, 1, 5, 3] and an experiment (3, 0.6). After such an experiment with the probability of 60\% the permutation will assume the form [1, 2, 4, 5, 3] and with a 40\% probability it will remain unchanged.

You have to determine the probability of the permutation becoming completely sorted in ascending order after m experiments.

Input

Each test contains one or more test cases. The first line contains the number of test cases t (1 ≤ t ≤ 100).

The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 10^5) — the length of the permutation and the number of experiments, respectively.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n) — contents of the permutation.

The following m lines of each test case each contain an integer r_i and a real number p_i (1 ≤ r_i ≤ n, 0 ≤ p_i ≤ 1) — the length of the prefix and the probability of it being sorted. All probabilities are given with at most 6 decimal places.

It is guaranteed that the sum of n and the sum of m does not exceed 10^5 (∑ n, ∑ m ≤ 10^5).

Output

For each test case, print a single number — the probability that after all experiments the permutation becomes sorted in ascending order. Your answer will be considered correct if its absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is accepted if and only if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.

Example

Input


4
4 3
4 3 2 1
1 0.3
3 1
4 0.6
5 3
4 2 1 3 5
3 0.8
4 0.6
5 0.3
6 5
1 3 2 4 5 6
4 0.9
5 0.3
2 0.4
6 0.7
3 0.5
4 2
1 2 3 4
2 0.5
4 0.1


Output


0.600000
0.720000
0.989500
1.000000

Note

Explanation of the first test case: It can be demonstrated that whether the final permutation is sorted or not depends solely on sorting being performed in the (4, 0.6) experiment.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.Writer;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author MaxHeap
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    CRandomEvents solver = new CRandomEvents();
    int testCount = Integer.parseInt(in.next());
    for (int i = 1; i <= testCount; i++) {
      solver.solve(i, in, out);
    }
    out.close();
  }

  static class CRandomEvents {

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt(), q = in.nextInt();
      int[] a = in.nextIntArray(n);
      int index = n;
      for (int i = n - 1; i >= 0; --i) {
        if (index != a[i]) {
          break;
        }
        --index;
      }
      double ans = 1.0;
      for (int i = 0; i < q; ++i) {
        int r = in.nextInt();
        double p = in.nextDouble();
        if (r >= index) {
          ans *= (1.0 - p);
        }
      }
      if (index == 0) {
        out.printf("%.6f\n", 1.0);
        return;
      }
      out.printf("%.6f\n", 1.0 - ans);
    }

  }

  static class OutputWriter extends PrintWriter {

    public OutputWriter(OutputStream out) {
      super(out);
    }

    public OutputWriter(Writer out) {
      super(out);
    }

    public OutputWriter(File file) throws FileNotFoundException {
      super(file);
    }

    public void close() {
      super.close();
    }

  }

  static class InputReader {

    private InputStream stream;
    private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
    private static final int EOF = -1;
    private byte[] buf = new byte[DEFAULT_BUFFER_SIZE];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {
      if (this.numChars == EOF) {
        throw new UnknownError();
      } else {
        if (this.curChar >= this.numChars) {
          this.curChar = 0;

          try {
            this.numChars = this.stream.read(this.buf);
          } catch (IOException ex) {
            throw new InputMismatchException();
          }

          if (this.numChars <= 0) {
            return EOF;
          }
        }

        return this.buf[this.curChar++];
      }
    }

    public int nextInt() {
      int c;
      for (c = this.read(); isSpaceChar(c); c = this.read()) {
      }

      byte sgn = 1;
      if (c == 45) {
        sgn = -1;
        c = this.read();
      }

      int res = 0;

      while (c >= 48 && c <= 57) {
        res *= 10;
        res += c - 48;
        c = this.read();
        if (isSpaceChar(c)) {
          return res * sgn;
        }
      }

      throw new InputMismatchException();
    }

    public double nextDouble() {
      double ret = 0, div = 1;
      int c = read();
      while (c <= ' ') {
        c = read();
      }
      boolean neg = (c == '-');
      if (neg) {
        c = read();
      }

      do {
        ret = ret * 10 + c - '0';
      }
      while ((c = read()) >= '0' && c <= '9');

      if (c == '.') {
        while ((c = read()) >= '0' && c <= '9') {
          ret += (c - '0') / (div *= 10);
        }
      }

      if (neg) {
        return -ret;
      }
      return ret;
    }

    public String next() {
      int c;
      while (isSpaceChar(c = this.read())) {
      }

      StringBuilder result = new StringBuilder();
      result.appendCodePoint(c);

      while (!isSpaceChar(c = this.read())) {
        result.appendCodePoint(c);
      }

      return result.toString();
    }

    public static boolean isSpaceChar(int c) {
      return c == 32 || c == 10 || c == 13 || c == 9 || c == EOF;
    }

    public int[] nextIntArray(int n) {
      int[] arr = new int[n];
      for (int i = 0; i < n; i++) {
        arr[i] = nextInt();
      }
      return arr;
    }

  }
}