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 <iostream>
#include <string>
#include <algorithm>
using namespace std;
#define rep(i,n) for((i)=0;(i)<(n);(i)++)
#define max(a,b) ((a)>(b) ? (a) : (b))
#define min(a,b) ((a)<(b) ? (a) : (b))
typedef long long ll;
typedef long double ld;
#define MOD1 1000000007
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
int main(){
  ll n,m,k,i,j,result=0,l=0,r=0;
  ll a[200010];
  cin >> n >> k;
  rep(i,n) cin >> a[i];
  sort(a,a+n);
  r=n-1;
  if(k%2==1){
    result = a[r];
    r--;
    k--;
    m=(result<0 ? -1 : 1);
  }else{
    result = 1;
    m = 1;
  }
  while(k>0){
    i = a[l]*a[l+1];
    j = a[r]*a[r-1];
    //cout << i << " " << j << endl;
    if(i*m>j*m){
      result *= i % MOD1;
      result %= MOD1;
      l += 2;
    }else{
      result *= j % MOD1;
      result %= MOD1;
      r -= 2;
    }
    k -= 2;
  }
  cout << (result+MOD1) % MOD1 << endl;
  return 0;
}