We have N bulbs arranged on a number line, numbered 1 to N from left to right. Bulb i is at coordinate i.

Each bulb has a non-negative integer parameter called intensity. When there is a bulb of intensity d at coordinate x, the bulb illuminates the segment from coordinate x-d-0.5 to x+d+0.5. Initially, the intensity of Bulb i is A_i. We will now do the following operation K times in a row:

* For each integer i between 1 and N (inclusive), let B_i be the number of bulbs illuminating coordinate i. Then, change the intensity of each bulb i to B_i.



Find the intensity of each bulb after the K operations.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 2 \times 10^5
* 0 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \ldots A_N


Output

Print the intensity A{'}_i of each bulb i after the K operations to Standard Output in the following format:


A{'}_1 A{'}_2 \ldots A{'}_N

Output

Print the intensity A{'}_i of each bulb i after the K operations to Standard Output in the following format:


A{'}_1 A{'}_2 \ldots A{'}_N

Examples

Input

5 1
1 0 0 1 0


Output

1 2 2 1 2


Input

5 2
1 0 0 1 0


Output

3 3 4 4 3
#include<bits/stdc++.h>
using namespace std;
typedef int int_t;

int_t A[200010], B[200010];

int main() {
    int_t n, k; scanf("%d%d", &n, &k);
    for(int_t i=1;i<=n;i++) scanf("%d", &A[i]);
    for(int_t i=1;i<=k;i++) {
        memset(B, 0, sizeof B);
        for(int_t j=1;j<=n;j++) B[max(1, j - A[j])] ++, B[min(n, j + A[j]) + 1] --;
        for(int_t j=1;j<=n;j++) A[j] = A[j-1] + B[j];
        bool ok = true;
        for(int_t j=1;j<=n;j++) if(A[j] < n) ok = false;
        if(ok) break;
    }
    for(int_t i=1;i<=n;i++) cout << A[i] << " ";
}