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 PYTHON3):

Solution:
import sys

def main():
    def modst(a, s):
        ret = 1
        while s:
            if s % 2:
                ret = ret * a % mod
            a = a * a % mod
            s //= 2
        return ret   
    def Cnk(n, k):
        return (k <= n and n >= 0) * ((f[n] * modst((f[k] * f[n - k]) % mod, mod - 2)) % mod)
    #x, y = map(int, sys.stdin.readline().split())
    n, m = map(int, sys.stdin.readline().split())
    #n = int(sys.stdin.readline().strip())
    #a, w = map(int, sys.stdin.readline().split())
    q = list(map(int, sys.stdin.readline().split())) 
    #q = sorted(list(map(int, sys.stdin.readline().split())), reverse=True)
    '''mod = 998244353
    f = [1, 1]
    for i in range(2, 200007):
        f.append((f[-1] * i) % mod)
    a = 0
    for i in range(2 - n % 2, n + 1, 2):
        a = (a + Cnk(max(((n - i) // 2) + i - 1, 0), i - 1)) % mod
    print((a * modst(modst(2, n), mod - 2)) % mod)'''
    
    p, ans, i = n, 1, n - 1
    while i > -1 and q[i] == i + 1:
        p, i = i, i - 1
    for i in range(m):
        a, b = map(float, input().split())
        if a >= p:
            ans = ans * (1 - b)
    print(1 - ans if p != 0 else 1)
        
                
            
        
        
    
    
            
    
    
         
for i in range(int(input())):
    main()