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)

//  RAKSHIT KADAM
//ALWAYS USE &IT FOR ITERATING USING AUTO ...
//USE COUNT(STARTING ADDRESS, ENDING ADRESS ,VALUE) FOR FINDING THE COUNT IN THE RESPECTIVE DATA STRUCTURE
//NOTE THAT MEMSET CANT FILL THE DOUBLE VALUES;
//ACCUMULATE DOES NOT WORK PROPERLY IF VALUES START SUMMING BEYOND 1E9...
 #include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
// #define ordered_set tree< int ,  null_type ,  less<int> ,  rb_tree_tag ,  tree_order_statistics_node_update>
#warning !!!check the size of arrayss!!!

// NUMERIC DEFINITIONS :
    #define INF 100000000000000005
    #define inf 1000000000
    #define MOD  1000000007
    #define newMOD  998244353
    #define MAX 300006
    #define pi 3.1415926535897932384626433832795
#define ld long double
 #define ll long long
 #define int long long

 #define P(gg) for(auto rax:gg){cout<<rax<<" ";}cout<<endl;
 #define Need_for_speed(activated) ios_base :: sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)
 #define satisfy ll t; cin>> t; while(t--)
 #define inp(n) int n;cin >> n
 #define mp make_pair
 #define pb push_back
 #define endl "\n"
 #define x first
 #define y second
 #define fore(i,a,b) for(ll i=a;i<b;i++)
 #define forci(i,n) for(ll i=0;i<n;i++)
 #define vi vector<ll>
 #define Endl endl
 #define lb lower_bound
 #define ub upper_bound
#define pii pair<ll,ll>

 #define input freopen("input.txt", "r", stdin),freopen("output.txt", "w", stdout)
 #define time        cerr << "\nTime elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n";
using namespace std;

ll gcd(ll a, ll b){if (b == 0)return a;return gcd(b, a % b);}
int power(int x, unsigned int y, unsigned int m){ if (y == 0) return 1;int p = power(x, y/2, m) % m;  p = (p * p) % m;return (y%2 == 0)? p : (x * p) % m;}
ll modInverse(int a, int m){{ return power(a, m-2, m);}}
const int maxn = 500003;
 
void solve()
{
    ll n,k;cin>>n>>k;
    ll a[n];ll dis[maxn];memset(dis,0,sizeof dis);
    for(ll j=0;j<k;j++)
    {
    for(ll i=0;i<n;i++)
    {
       if(!j) cin>>a[i];
        
        ll l = max(0LL,i-a[i]);
        ll r =min(n-1,i+a[i]);
        
        dis[l]++;dis[r+1]--;
    }
        for(ll i=0;i<n;i++)
        {
            a[i] = dis[i];
            if(i){a[i]+=dis[i-1];dis[i]+=dis[i-1];}
        }
        ll cnt =0;
        for(ll i=0;i<n;i++){if(a[i]==n)cnt++;dis[i]=0;}
        if(cnt==n)
        {
            for(ll i=0;i<n;i++)cout<<n<<" ";
            cout<<Endl;return;
        }
    }
    for(ll i=0;i<n;i++)cout<<a[i]<<" ";cout<<endl;
}

signed main()
{
   Need_for_speed(activated);
//
//satisfy
//    {
//  solve();
//   }

    solve();
    
    return 0;
}