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 <bits/stdc++.h>
using namespace std;
#define ll long long
#define rep(i, n) for (int i = 0; i < n; i++)
#include <math.h> /* M_PI */
#define INF 2147483647
/*
 add(a,b,x): [a,b) にxを加算する。
 getSum(a,b):[a,b)の区間の合計を取得する。log オーダー 
 
*/

ll N, Q;
struct LazySegmentTree
{
private:
    int n;
    vector<ll> node, lazy;

public:
    LazySegmentTree(vector<ll> v)
    {
        int sz = (int)v.size();
        n = 1;
        while (n < sz)
            n *= 2;
        node.resize(2 * n - 1);
        lazy.resize(2 * n - 1, 0);

        for (int i = 0; i < sz; i++)
            node[i + n - 1] = v[i];
        for (int i = n - 2; i >= 0; i--)
            node[i] = node[i * 2 + 1] + node[i * 2 + 2];
    }

    void eval(int k, int l, int r)
    {
        if (lazy[k] != 0)
        {
            node[k] += lazy[k];
            if (r - l > 1)
            {
                lazy[2 * k + 1] += lazy[k] / 2;
                lazy[2 * k + 2] += lazy[k] / 2;
            }
            lazy[k] = 0;
        }
    }

    void add(int a, int b, ll x, int k = 0, int l = 0, int r = -1)
    {
        if (r < 0)
            r = n;
        eval(k, l, r);
        if (b <= l || r <= a)
            return;
        if (a <= l && r <= b)
        {
            lazy[k] += (r - l) * x;
            eval(k, l, r);
        }
        else
        {
            add(a, b, x, 2 * k + 1, l, (l + r) / 2);
            add(a, b, x, 2 * k + 2, (l + r) / 2, r);
            node[k] = node[2 * k + 1] + node[2 * k + 2];
        }
    }

    ll getsum(int a, int b, int k = 0, int l = 0, int r = -1)
    {
        if (r < 0)
            r = n;
        eval(k, l, r);
        if (b <= l || r <= a)
            return 0;
        if (a <= l && r <= b)
            return node[k];
        ll vl = getsum(a, b, 2 * k + 1, l, (l + r) / 2);
        ll vr = getsum(a, b, 2 * k + 2, (l + r) / 2, r);
        return vl + vr;
    }
};

int main()
{
    ll n, k;
    cin >> n >> k;
    vector<ll> A(n);
    rep(i, n)
    {
        cin >> A[i];
    }
    LazySegmentTree seg(vector<ll>(n, 0));
    LazySegmentTree seg2(vector<ll>(n, 0));
    LazySegmentTree seg3(vector<ll>(n, 0));
    rep(i, n)
    {
        seg.add(i, i + 1, A[i]); //ここに入れておく
                                 // cout << seg.getsum(i, i + 1) << endl;
    }
    rep(i, n)
    {
        //seg2 = seg;
        // cout << seg.getsum(i, i + 1) << endl;
    }
    ll y = 0;
    int flag = 1;
    rep(i, k)
    {
        flag = 1;
        rep(j, n)
        {

            ll p = seg.getsum(j, j + 1);
            seg2.add(max((ll)0, j - p), min(n, j + p + 1), 1);

            if (j == 0)
            {
                y = p;
                if (i == k - 1)
                {
                    //cout << y << " " << n;
                }
                if (y != n)
                {
                    flag = 0;
                }
            }
            else
            {
                if (y == n)
                {
                    if (y != p)
                    {
                        //cout << "4da3";
                        flag = 0;
                    }
                }
            }
            if (flag == 1)
            {
                rep(g, n)
                {
                    // cout << "dafa";
                    cout << seg.getsum(g, g + 1) << " ";
                }
                break;
            }
        }
        if (flag == 1)
        {
            break;
        }
        seg = seg2;
        seg2 = seg3;
    }
    if (flag == 0)
    {
        rep(g, n)
        {
            // cout << "dafa";
            cout << seg.getsum(g, g + 1) << " ";
        }
    }
}