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 <algorithm>
#include <cstdio>
using namespace std;
int n, k;
long long int a[200005], s[200005], ps = 0;
const long long MOD = 1e9 + 7;
int main() {
  scanf("%d %d", &n, &k);
  long long res = 1;
  for (int i = 0; i < n; ++i) {
    scanf("%lld", &a[i]);
  }
  sort(a, a + n);

  if (k % 2) {
    res = a[n - 1];
    int w = res > 0 ? 1 : -1;
    int l = 0, r = n - 2, cnt = 1;
    while (cnt < k && l < r) {
      if (w * a[l] * a[l + 1] > w * a[r] * a[r - 1]) {
        s[ps++] = a[l++];
        s[ps++] = a[l++];
        cnt += 2;
      } else {
        s[ps++] = a[r--];
        s[ps++] = a[r--];
        cnt += 2;
      }
    }
  } else {
    res = 1;
    int l = 0, r = n - 1, cnt = 0;
    while (cnt < k && l < r) {
      if (a[l] * a[l + 1] > a[r] * a[r - 1]) {
        s[ps++] = a[l++];
        s[ps++] = a[l++];
        cnt += 2;
      } else {
        s[ps++] = a[r--];
        s[ps++] = a[r--];
        cnt += 2;
      }
    }
  }
  for (int i = 0; i < ps; ++i) {
    res = (1l * (s[i] % MOD) * (res % MOD) + MOD) % MOD;
  }
  res = (res % MOD + MOD) % MOD;
  printf("%lld\n", res);
  return 0;
}
