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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

#define ll long long


					
int main()
{
	#ifndef	ONLINE_JUDGE
		freopen("input.txt", "r",stdin);
	#endif 
	ios_base::sync_with_stdio();
	cin.tie(0);
	cout.tie(0);
	int t;
	ll m,n,idx;
	cin>>t;
	long double f;
	ll x;
	long double prob,y;
	vector<ll> a,b;
	while(t--)
	{
		cin>>n>>m;
		a.clear();
		b.clear();
		a.resize(n);
		b.resize(n);
		for(int i=0;i<n;i++)
		{
			cin>>a[i];
			b[i]=a[i];
		}
		idx=-1;
		sort(b.begin(),b.end());
		for(int j=n-1;j>=0;j--)
		{
			if(a[j]!=b[j])
			{
				idx = j;
				break;
			}
		}
		idx++;
		if(!idx)
		{	
			f=1.00;
			cout<<fixed<<setprecision(15)<<f;
			cout<<'\n';
		}
		prob=1.00;
		while(m--)
		{
			cin>>x;
			cin>>y;
			if(x<idx)
			{
				continue;
			}
			else
			{
				prob*=(1-y);
			}
		}
		if(!idx)
		{
			continue;
		}
		prob = 1-prob;
		cout<<fixed<<setprecision(6)<<prob<<'\n';
	}
	return 0;
}