Problem:
Score : 500 points

Problem Statement

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

Sample Input 1

5 1
1 0 0 1 0

Sample Output 1

1 2 2 1 2

Initially, only Bulb 1 illuminates coordinate 1, so the intensity of Bulb 1 becomes 1 after the operation.
Similarly, the bulbs initially illuminating coordinate 2 are Bulb 1 and 2, so the intensity of Bulb 2 becomes 2.

Sample Input 2

5 2
1 0 0 1 0

Sample Output 2

3 3 4 4 3

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(begin, end) for (i=begin;i<end;i++)
#define repj(begin, end) for (j=begin;j<end;j++)
#define init(arr, end, val) for (i=0;i<end;i++) arr[i] = val;
#define printint(i0, i1) printf("%d %d\n", i0, i1)

using namespace std;
typedef long long int ll;
const int inf = 1000000000;
const int mod = 1000000007;
const int nil = -1;
int i, j, n, m, k, ans;
int a[200000];
int b[200000];

int main() {
    scanf(" %d %d", &n, &k);
    rep(0,n) {
        scanf(" %d", &a[i]);
    }
    repj(0,k) {
        rep(0, n) b[i] = 0;
        rep(0, n) {
            int l = max(0, i-a[i]);
            int r = min(n-1, i+a[i]);
            b[l]++;
            if (r+1<n) b[r+1]--;
        }
        bool saturated = b[0] == n;
        a[0] = b[0];
        rep(1,n) {
            b[i]+=b[i-1];
            a[i] = b[i];
            saturated = saturated && b[i] == n;
        }
        if (saturated) break;
    }

    rep(0, n) printf("%d ", b[i]);
    printf("\n");
}