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 CPP):

Solution:
#include<bits/stdc++.h>

#define Rushia_mywife ios::sync_with_stdio(0);cin.tie(0);
#define F first
#define S second
#define FF first.first
#define FS first.second
#define SF second.first
#define SS second.second
#define pb push_back
#define pob pop_back
#define pf push_front
#define pof pop_front
#define all(x) (x).begin(),(x).end()
#define mem(x,i) memset((x),(i),sizeof((x)))

using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<long long,long long>;
using ld = long double;

const int mod = 1000000007;
const int hnum = 998244353;
const ld PI = acos(-1);

#define Bint __int128
#define int long long
int qpow(int x,int powcnt,int tomod){
	int res = 1;
	for(;powcnt;powcnt>>=1,x=(x*x)%tomod)
		if(1&powcnt)res = (res*x)%tomod;
	return (res%tomod);
}
int inv(int x){ return qpow(x,mod-2,mod); }
// --------------------------------------**
const int N = 1e5+10;

int n,m;
int a[N];

void solve(){
	cin >> n >> m;
	for(int i=1;i<=n;i++)
		cin >> a[i];
	int tp = n;
	for(int i=n;i;i--,tp--)
		if(a[i]!=i)
			break;
	ld ans = 1;
	for(int i=0,x;i<m;i++){
		ld p;
		cin >> x >> p;
		if(x>=tp)
			ans *= (1-p);
	}
	if(tp==0){
		cout << "1.000000\n";
		return;
	}
	cout << fixed << setprecision(6) << 1-ans << '\n';
}

signed main(){
    Rushia_mywife
    int t = 1; 
    cin >> t;
    while(t--)
        solve();
}