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)

#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<vector>
#include<functional>
#include<algorithm>
#include<stdlib.h>
#include<string>
#include<string.h>
#define _USE_MATH_DEFINES
#include<math.h>
#include<deque>
#include<set>
#include<map>
#include<queue>
#include<list>
#include<iostream>
#include <bitset>
using namespace std;
typedef long long ll;
#define rep(i,a,b) for(auto i=a;i<b;i++)
#define all(_x) _x.begin(), _x.end()
#define r_sort(_x) sort(_x.begin(), _x.end(), std::greater<int>())
#define vec_cnt(_a, _n) (upper_bound(all(_a), _n) - lower_bound(all(_a), _n))
#define vec_unique(_a) _a.erase(std::unique(all(_a)), _a.end());
#define vvec vector<vector<ll>>
ll gcd(ll a, ll b) { return a % b == 0 ? b : gcd(b, a % b); }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }
#define INF 1 << 30
const int mod = 1000000007;
ll power(ll x, ll p) { ll a = 1; while (p > 0) { if (p % 2 == 0) { x *= x; p /= 2; } else { a *= x; p--; } }return a; }
ll mpower(ll x, ll p) { ll a = 1; while (p > 0) { if (p % 2 == 0) { x = x * x % mod; p /= 2; } else { a = a * x % mod; p--; } }return a; }
ll ac(ll n, ll k) { ll a = 1; rep(i, 1, k) { a *= n - i + 1; a /= i; }return a; }
ll mc(ll n, ll m) { ll k = 1, l = 1; rep(i, n - m + 1, n + 1) k = k * i % mod; rep(i, 1, m + 1) l = l * i % mod; l = mpower(l, mod - 2); return k * l % mod; }

int main()
{
	int N, k;
	cin >> N >> k;
	vector<int> A(N), imos(N), d(N);
	rep(i, 0, N) {
		cin >> A[i];
		imos[max(i - A[i], 0)]++;
		if (i + A[i] + 1 < N)imos[i + A[i] + 1]--;
	}
	rep(i, 0, N - 1)imos[i + 1] += imos[i];
	int D;
	rep(_i, 0, k) {
		rep(i, 0, N) {
			d[i] = imos[i] - A[i];
		}
		D = _i;
		rep(i, 1, N) {
			if (d[i] != d[0]) {
				D = -1;
				break;
			}
		}
		if (D == _i)break;
		rep(i, 0, N) {
			rep(i2, 1, d[i]) {
				if (i - A[i] - i2 >= 0)imos[i - A[i] - i2]++;
				if (i + A[i] + i2 < N)imos[i + A[i] + i2]++;
			}
			A[i] += d[i];
		}
	}
	if (D == -1)D = k;
	rep(i, 0, N) {
		printf(i == N - 1 ? "%d\n" : "%d ", A[i] + d[0] * (k - D));
	}
	return 0;
}