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).

<image>

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.*;
import java.util.*;

@SuppressWarnings("unchecked")
public class RandomEvents implements Runnable {

		void solve() throws IOException {
			int t = ri();
			while( t--> 0 ){
				int n = ri(), m = ri();

				int[] arr= iArr(n);
				for(int i = 0;i < n ;i++){
					arr[i] = ri();
				}

				int last = -1;
				for(int i = n - 1; i >= 0; i--){
					if( arr[i] != (i + 1) ){
						last = i;
						break;
					}
				}
				double total = 1;
				boolean isFound = false;

				for(int i = 0; i < m; i++){
					int index = ri() - 1; double p = rd();
					if( last != -1 && index >= last ){
						isFound = true;
						total *= (1 - p);
					}
				}

				if(isFound){println( String.format("%.6f", ( 1 - total) ));}
				else if(!isFound && last != -1) println(String.format("%.6f", ((double)0)));
				else println(String.format("%.6f", ((double)1)));
			}
		}


		/************************************************************************************************************************************************/
		public static void main(String[] args) throws IOException {
			new Thread(null, new RandomEvents(), "1").start();
		}

		static PrintWriter out = new PrintWriter(System.out);
		static Reader read = new Reader();
		static StringBuilder sbr = new StringBuilder();
		static int mod = (int) 1e9 + 7;
		static int dmax = Integer.MAX_VALUE;
		static long lmax = Long.MAX_VALUE;
		static int dmin = Integer.MIN_VALUE;
		static long lmin = Long.MIN_VALUE;

		@Override
		public void run() {
			try {
				println(" ");
				solve();
				out.close();
			} catch (IOException e) {
				e.printStackTrace();
				System.exit(1);
			}
		}

		static class Reader {
			private byte[] buf = new byte[1024];
			private int index;
			private InputStream in;
			private int total;

			public Reader() {
				in = System.in;
			}

			public int scan() throws IOException {
				if (total < 0)
					throw new InputMismatchException();
				if (index >= total) {
					index = 0;
					total = in.read(buf);
					if (total <= 0)
						return -1;
				}
				return buf[index++];
			}

			public int intNext() throws IOException {
				int integer = 0;
				int n = scan();
				while (isWhiteSpace(n))
					n = scan();
				int neg = 1;
				if (n == '-') {
					neg = -1;
					n = scan();
				}
				while (!isWhiteSpace(n)) {
					if (n >= '0' && n <= '9') {
						integer *= 10;
						integer += n - '0';
						n = scan();
					} else throw new InputMismatchException();
				}
				return neg * integer;
			}

			public double doubleNext() throws IOException {
				double doub = 0;
				int n = scan();
				while (isWhiteSpace(n))
					n = scan();
				int neg = 1;
				if (n == '-') {
					neg = -1;
					n = scan();
				}
				while (!isWhiteSpace(n) && n != '.') {
					if (n >= '0' && n <= '9') {
						doub *= 10;
						doub += n - '0';
						n = scan();
					} else throw new InputMismatchException();
				}
				if (n == '.') {
					n = scan();
					double temp = 1;
					while (!isWhiteSpace(n)) {
						if (n >= '0' && n <= '9') {
							temp /= 10;
							doub += (n - '0') * temp;
							n = scan();
						} else throw new InputMismatchException();
					}
				}
				return doub * neg;
			}

			public String read() throws IOException {
				StringBuilder sb = new StringBuilder();
				int n = scan();
				while (isWhiteSpace(n))
					n = scan();
				while (!isWhiteSpace(n)) {
					sb.append((char) n);
					n = scan();
				}
				return sb.toString();
			}

			private boolean isWhiteSpace(int n) {
				if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1)
					return true;
				return false;
			}
		}

		static void shuffle(int[] aa) {
			int n = aa.length;
			Random rand = new Random();
			for (int i = 1; i < n; i++) {
				int j = rand.nextInt(i + 1);
				int tmp = aa[i];
				aa[i] = aa[j];
				aa[j] = tmp;
			}
		}

		static void shuffle(int[][] aa) {
			int n = aa.length;
			Random rand = new Random();
			for (int i = 1; i < n; i++) {
				int j = rand.nextInt(i + 1);
				int first = aa[i][0];
				int second = aa[i][1];
				aa[i][0] = aa[j][0];
				aa[i][1] = aa[j][1];
				aa[j][0] = first;
				aa[j][1] = second;
			}
		}

		static final class Comparators {
			public static final Comparator<int[]> pairIntArr =
				(x, y) -> x[0] == y[0] ? compare(x[1], y[1]) : compare(x[0], y[0]);

			private static final int compare(final int x, final int y) {
				return Integer.compare(x, y);
			}
		}


		static void print(Object object) {
			out.print(object);
		}

		static void println(Object object) {
			out.println(object);
		}


		static int[] iArr(int len) {
			return new int[len];
		}

		static long[] lArr(int len) {
			return new long[len];
		}

		static long min(long a, long b) {
			return Math.min(a, b);
		}

		static int min(int a, int b) {
			return Math.min(a, b);
		}

		static long max(Long a, Long b) {
			return Math.max(a, b);
		}

		static int max(int a, int b) {
			return Math.max(a, b);
		}

		static int ri() throws IOException {
			return read.intNext();
		}

		static long rl() throws IOException {
			return Long.parseLong(read.read());
		}

		static String rs() throws IOException {
			return read.read();
		}	

		static double rd() throws IOException {
			return read.doubleNext();
		}	
}