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>

#define M_PI       3.14159265358979323846   // pi

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<ll> VI;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;

#define rep(a,n) for(ll a = 0;a < n;a++)
#define repi(a,b,n) for(ll a = b;a < n;a++)

using namespace std;

static const ll INF = 1e15;

const ll mod = 1000000007;


int main() {
	ll n, k;
	cin >> n >> k;
	vector<ll> vs(n);
	rep(i, n) {
		cin >> vs[i];
	}
	sort(vs.begin(), vs.end());
	ll ans = 1;
	ll right = n - 1;
	ll left = 0;
	int sign = 1;
	if (k % 2) {
		ans = vs[n - 1];
		right--;
		if (ans < 0) {
			sign = -1;
		}
		k--;
	}
	while (k > 0) {
		ll c1 = vs[right] * vs[right - 1];
		ll c2 = vs[left] * vs[left + 1];
		if (c1 * sign >= c2 * sign) {
			ans *= c1 % mod;
			ans %= mod;
			right -= 2;			
		}
		else {
			ans *= c2 % mod;
			ans %= mod;
			left += 2;
		}
		k -= 2;
	}
	cout << (ans + mod) % mod<< endl;
	return 0;
}
