#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<tuple>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define Per(i,sta,n) for(int i=n-1;i>=sta;i--)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};

int n,k;
int p[100010];
vector<int> G[100010],R[100010];
bool going[100010],backing[100010];
vector<int> cycle[100010];
vector<ll> cycle_S[100010];
int comp_idx[100010],cycle_idx[100010];
bool isCycle[100010];
ll ans[100010];
ll depth[100010];

int dfs(int s,vector<int> &hist){
    //cout << s << endl;
    if(going[s]) return -1;
    going[s]=true;
    hist.push_back(s);
    int res=-1;
    for(int t:G[s]){
        if(backing[t])continue;
        if(going[t]){
            return t;
        }
        res=dfs(t,hist);
        if(res!=-1) return res;
    }
    hist.pop_back();
    backing[s]=true;
    return -1;
}

void rdfs(int s,vector<int> &v,ll dep,int id){
    if(ans[s]!=-1) return;
    comp_idx[s]=id;
    //cout << s << endl;
    v.push_back(s);
    if(v.size()!=1)depth[s]=dep+p[s];
    int d=v.size()-1;
    int siz=cycle[comp_idx[s]].size();
    if(d-k-1<0){
        ans[s]=depth[s];
        ll m=k-d;
        int sta=cycle_idx[v[0]];
        ll gol=sta+m;
        //cout << sta << " " << gol << endl;
        if(gol<siz){
            ans[s]+=cycle_S[comp_idx[s]][gol]-cycle_S[comp_idx[s]][sta];
        }
        else{
            ans[s]+=cycle_S[comp_idx[s]][siz]-cycle_S[comp_idx[s]][sta]+cycle_S[comp_idx[s]][gol%siz]+(ll)(gol/siz-1)*cycle_S[comp_idx[s]].back();
        }
    }
    else{
        ans[s]=depth[s]-depth[v[d-k-1]];
    }
    for(int t:R[s]){
        if(isCycle[t]) continue;
        rdfs(t,v,depth[s],id);
    }
    v.pop_back();
}

void solve(){
    cin >> n >> k;
    rep(i,n){
        cin >> p[i];
        G[i].push_back((i+p[i])%n);
        R[(i+p[i])%n].push_back(i);
        comp_idx[i]=-1;
        cycle_idx[i]=-1;
        ans[i]=-1;
    }
    int id=0;
    rep(i,n){
        if(backing[i]) continue;
        vector<int> hist={};
        int t=dfs(i,hist);
        int l=0;
        bool cy=false;
        if(t!=-1){
            cycle_S[id].push_back(0);
            for(int c:hist){
                if(!cy && c==t){
                    cy=true;
                }
                else if(!cy){
                    continue;
                }
                //cout << c << " ";
                cycle[id].push_back(c);
                cycle_S[id].push_back(cycle_S[id].back()+p[c]);
                isCycle[c]=true;
                cycle_idx[c]=l;
                comp_idx[c]=id;
                l++;
            }
            // cout << "" << endl;
            // for(int s:cycle_S[id]){
            //     cout << s << " ";
            // }
            // cout << "" << endl;
            id++;
        }
    }
    // rep(i,n){
    //     cout << i << " " << comp_idx[i] << " " << cycle_idx[i] << endl;
    // }
    rep(i,n){
        vector<int> v(0);
        if(isCycle[i]) rdfs(i,v,0,comp_idx[i]);
    }
    rep(i,n){
        cout << i+1+ans[i] << endl;
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(50);
    solve();
}