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:
/*
ID: Trump
TASK: 
LANG: C++
*/
/* LANG can be C++11 or C++14 for those more recent releases */
#include <iostream>
#include <fstream>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
typedef long double lb;
typedef double db;
typedef int it;
//#define MARK
const ll losn=1e6+5;
const ll maxn=1e5+5;
const ll minn=1e3+5;
const ll tiny=1e2+5;
const ll inf=1e9;
const ll binf=1e18;
const ll mod=1e9+7;
const ll hmod=4698571;
const lb pi=3.1415926;
const ll myn=0;
void gk(){cout<<"---------------"<<endl;}
void ck(){cout<<1<<endl;}
void ck(ll a){cout<<a<<endl;}
void ck(ll a[minn][minn],ll n,ll m){for(ll i=1;i<=n;i++){for(ll j=1;j<=m;j++){cout<<a[i][j]<<" ";}cout<<endl;}}
ll n,m,k,T,u,v,len;

lb arr[maxn];
lb a[maxn],b[maxn];
int main(){
//#ifdef MARK
//    freopen("input.in", "r", stdin);
//    freopen("ouput.out", "w", stdout);
//    freopen("input.in", "r", stdin);
//    freopen("ouput.out", "w", stdout);
//#endif
	ll t;
	cin>>t;
	while(t--){
		cin>>n>>m;
		for(ll i=1;i<=n;i++){
			cin>>arr[i];
		}
		/*
		0 10
		6 4
		7.2
		*/
		lb ld=n;
		for(lb i=n;i>=1;i--){
			if(arr[(ll)i]==i){
				ld--;
			}else{
				break;
			}
		}
		for(ll i=1;i<=m;i++){
			cin>>a[i]>>b[i];
		}
		lb le=0,re=10;
		if(ld==0){
			le=10;
			re=0;
		}
		for(ll i=1;i<=m;i++){
			if(a[i]>=ld){
				lb left=re*b[i];
				le+=left;
				re-=left;
			}
		}
		printf("%.6Lf\n",le/(10*1.0));
	}
	return 0;
}
/*
0 10
0 10
4 6


2
5 3
4 2 1 3 5
3 0.8
4 0.6
5 0.3
*/