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 PYTHON3):

Solution:
from collections import Counter, defaultdict, deque
import math
class newNode:  
  
    # Construct to create a newNode  
    def __init__(self, key):  
        self.data = key  
        self.left = None
        self.right = None
  
""" Function to print spiral traversal of a tree"""
def printSpiral(root): 
  
    h = height(root)  
      
    """ltr Left to Right. If this variable  
    is set, then the given level is traversed 
    from left to right. """
    ltr = False
    for i in range(1, h + 1): 
      
        printGivenLevel(root, i, ltr)  
  
        """Revert ltr to traverse next level 
           in opposite order"""
        ltr = not ltr  
      
""" Print nodes at a given level """
def printGivenLevel(root, level, ltr): 
  
    if(root == None): 
        return
    if(level == 1): 
        print(root.data, end = " ")  
    elif (level > 1): 
      
        if(ltr): 
            printGivenLevel(root.left, level - 1, ltr)  
            printGivenLevel(root.right, level - 1, ltr)  
          
        else: 
            printGivenLevel(root.right, level - 1, ltr)  
            printGivenLevel(root.left, level - 1, ltr)  
          
""" Compute the "height" of a tree -- the number of  
    nodes along the longest path from the root node  
    down to the farthest leaf node."""
def height(node): 
  
    if (node == None): 
        return 0
    else: 
      
        """ compute the height of each subtree """
        lheight = height(node.left)  
        rheight = height(node.right)  
  
        """ use the larger one """
        if (lheight > rheight): 
            return(lheight + 1)  
        else: 
            return(rheight + 1)  
      

def solve(n, m, arr, pro):
    for i in range(n, 0, -1):
        if arr[i-1] == i:
            i -= 1
        else:
            break
    minpos = i
    if minpos == 0:
        return 1
    #print(minpos)
    temp = 1
    ans = 0
    for i in range(0,m):
        if pro[i][0] >= minpos:
            ans += temp * pro[i][1]
            temp *= (1-pro[i][1])
    return ans

    
    

res = []
t = int(input())
for i in range(0,t):
    p=[]
    n, m = list(map(int, input().split()))
    a = list(map(int, input().split()))
    for i in range(0,m):
        s = input().split()
        p.append([int(s[0]), float(s[1])])
    res.append(solve(n, m, a, p))
for i in range(0,t):
    print(res[i])