You've got an array a, consisting of n integers. The array elements are indexed from 1 to n. Let's determine a two step operation like that:

  1. First we build by the array a an array s of partial sums, consisting of n elements. Element number i (1 ≤ i ≤ n) of array s equals <image>. The operation x mod y means that we take the remainder of the division of number x by number y. 
  2. Then we write the contents of the array s to the array a. Element number i (1 ≤ i ≤ n) of the array s becomes the i-th element of the array a (ai = si). 



You task is to find array a after exactly k described operations are applied.

Input

The first line contains two space-separated integers n and k (1 ≤ n ≤ 2000, 0 ≤ k ≤ 109). The next line contains n space-separated integers a1, a2, ..., an — elements of the array a (0 ≤ ai ≤ 109).

Output

Print n integers — elements of the array a after the operations are applied to it. Print the elements in the order of increasing of their indexes in the array a. Separate the printed numbers by spaces.

Examples

Input

3 1
1 2 3


Output

1 3 6


Input

5 0
3 14 15 92 6


Output

3 14 15 92 6
#include <bits/stdc++.h>
using namespace std;
int N, K;
long long int number[2000];
long long int result[2000];
long long int ansmatrix[2000][2000];
long long int tmpmatrix[2000][2000];
void matrixcopy() {
  int i, j;
  for (i = 0; i < N; i++) {
    long long int *ansptr = &ansmatrix[i][0];
    long long int *tmpptr = &tmpmatrix[i][0];
    for (j = 0; j <= i; j++) {
      *ansptr = *tmpptr;
      ansptr++;
      tmpptr++;
    }
  }
}
void matrixmul() {
  int i, j;
  for (i = 0; i < N; i++) {
    tmpmatrix[i][0] = 0;
    for (j = 0; j <= i; j++) {
      tmpmatrix[i][0] += ansmatrix[i][j] * ansmatrix[j][0];
      tmpmatrix[i][0] %= 1000000007;
    }
    for (j = 1; i + j < N; j++) tmpmatrix[i + j][j] = tmpmatrix[i][0];
  }
  matrixcopy();
}
void matrixmulone() {
  int i, j;
  for (i = 0; i < N; i++) {
    tmpmatrix[i][0] = 0;
    for (j = 0; j <= i; j++) {
      tmpmatrix[i][0] += ansmatrix[i][j];
      tmpmatrix[i][0] %= 1000000007;
    }
    for (j = 1; i + j < N; j++) tmpmatrix[i + j][j] = tmpmatrix[i][0];
  }
  matrixcopy();
}
void matrixpow(int powval) {
  if (powval == 1) return;
  matrixpow(powval / 2);
  matrixmul();
  if (powval % 2) {
    matrixmulone();
  }
}
int main() {
  int i, j;
  scanf("%d %d", &N, &K);
  for (i = 0; i < N; i++) scanf("%d", &number[i]);
  for (i = 0; i < N; i++) {
    for (j = 0; j <= i; j++) ansmatrix[i][j] = 1;
  }
  if (K != 0) matrixpow(K);
  if (K == 0) {
    for (i = 0; i < N; i++) printf("%I64d ", number[i]);
  } else {
    for (i = 0; i < N; i++) {
      result[i] = 0;
      for (j = 0; j < N; j++) {
        result[i] += ansmatrix[i][j] * number[j];
        result[i] %= 1000000007;
      }
      printf("%I64d ", result[i]);
    }
  }
  return 0;
}
