Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

* 1 \leq K \leq N \leq 2\times 10^5
* |A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 \ldots A_N


Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Examples

Input

4 2
1 2 -3 -4


Output

12


Input

4 3
-1 -2 -3 -4


Output

1000000001


Input

2 1
-1 1000000000


Output

1000000000


Input

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1


Output

999983200
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1E9 + 7;
long long solve(vector<long long> v, int k)
{
	int n = v.size();
	sort(v.begin(), v.end());
	long long pro = 1;
	if (v[n - 1] == 0 && (k & 1))
		return 0;
	if (v[n - 1] <= 0 && (k & 1))
	{
		for (int i = n - 1; i >= n - k; --i)
		{
			pro = ((pro * v[i]) % MOD + MOD) % MOD;
		}
		return pro;
	}
	long long i = 0, j = n - 1;
	if (k & 1)
	{
		pro *= v[j];
		j --;
		k --;
	}
	k >>= 1;
	for (int idx = 0; idx < k; ++idx)
	{
		long long lp = v[i] * v[i + 1];
		long long rp = v[j] * v[j - 1];
		if (lp > rp)
		{
			pro = ((pro * ((lp + MOD) % MOD)) % MOD + MOD) % MOD;
			i += 2;
		}
		else
		{
			pro = ((pro * ((rp + MOD) % MOD)) % MOD + MOD) % MOD;
			j -= 2;
		}
	}
	return pro;

}
int main(int argc, char const *argv[])
{
	int n, k;
	cin >> n >> k;
	vector<long long> a(n);
	for (int i = 0; i < n; ++i)
	{
		cin >> a[i];
	}
	cout << solve(a, k) << '\n';

	return 0;
}