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 REP(i, e) for(int (i) = 0; (i) < (e); ++(i))
#define FOR(i, b, e) for(int (i) = (b); (i) < (e); ++(i))
#define ALL(c) (c).begin(), (c).end()
#define PRINT(x) cout << (x) << "\n"
using namespace std;
using ll = long long; using pint = pair<int, int>; using pll = pair<ll, ll>;
template<typename T> auto compare = [](T x, T y) -> bool{return (x < y);};
const int MOD = 1000000007;

ll N, K;
ll A[200010];

signed main(){
    cin >> N >> K;
    REP(i, N) cin >> A[i];
    sort(A, A + N);
    ll ans = 1;
    if(A[N - 1] <= 0 && K % 2 == 1){
        for(int i = N - 1; i >= N - K; i--) ans = (ans * A[i]) % MOD;
        PRINT((ans + MOD) % MOD);
        return 0;
    }
    int l = 0, r = N - 1;
    if(K % 2 == 1){
        ans = (ans * A[r]) % MOD;
        r--; K--;
    }
    for(int i = 0; 2 * i < K; i++){
        if(A[l] * A[l + 1] >= A[r - 1] * A[r]){
            ans = (ans * ((A[l] * A[l + 1]) % MOD)) % MOD;
            l += 2;
        }else{
            ans = (ans * ((A[r - 1] * A[r]) % MOD)) % MOD;
            r -= 2;
        }
    }
    PRINT((ans + MOD) % MOD);
    return 0;
}