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: Wrong Answer)

#include <iostream>
#include <vector>
#include <utility>
#include <algorithm>

int main() {
    std::ios::sync_with_stdio(false);
    int n, k;
    std::cin >> n >> k;
    std::vector<double> bulbs(n);
    for (auto& v: bulbs) {
        std::cin >> v;
    }
    ;
    for (int i = 0; i < k; ++i) {
        bool is_changed = false;
        std::vector<std::pair<double, int>> points;
        for (int j = 0; j < n; ++j) {
            points.push_back({j - bulbs[j] - .5, -1});
            points.push_back({j, 0});
            points.push_back({j + bulbs[j] + .5, 1});
        }
        std::sort(begin(points), end(points));
        int cur = 0;
        for (auto p: points) {
            auto typ = p.second;
            auto coord = p.first;
            cur += typ;
            if (typ == 0 && bulbs[coord] != -cur) {
                bulbs[coord] = -cur;
                is_changed = true;
            }
        }
        if (!is_changed) {
            std::cout << "exit at " << i << std::endl;
            break;
        }
    }
    for (auto& v: bulbs) {
        std::cout << v << " ";
    }
    std::cout << std::endl;
    return 0;
}