#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

#define fast ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)
const ll mod = 1e9+7;

int bs(int c_idx, ll x, vector<ll> &pre, int n){

    int l = c_idx, r = 2*n, ans = -1;
    while(l<=r){
        int m = l + (r-l)/2;
        // cout<<"m: "<<m;
        if(x == pre[m] - pre[c_idx-1]){
            return m;
        }
        else if(x < pre[m] - pre[c_idx-1]){
            // cout<<" y: "<<m<<endl;

            r = m-1;
        }
        else{
            ans = m;
            l = m+1;
            // cout<<" n: "<<m<<endl;
        }
    }
    return ans;
}
int bins(ll space, int c_idx, int e_idx, vector<ll> &pre){
    int l = c_idx, r = e_idx, ans = -1;
    while(l<=r){
        int m = l + (r-l)/2;
        if(space >= pre[e_idx] - pre[m-1]){
            ans = m;
            r = m-1;
        }
        else{
            l = m+1;
        }
    }
    return ans;
}
int solve(){
    ll n,x;cin>>n>>x;
    vector<ll> d(n+1,0);
    vector<ll> pre(2*n+2, 0);
    vector<ll> mpre(2*n + 2, 0);

    for(int i=1;i<=n;++i){
        cin>>d[i];
    }
    d[0] = d[n], pre[0] = d[0], mpre[0] = (d[0]*(d[0]+1))/2;
    for(int i=1;i<=n;++i){
        pre[i] = pre[i-1] + d[i];
        mpre[i] = mpre[i-1] + (d[i]*(d[i]+1))/2;
    }

    for(int i=n+1;i<=n+n;++i){
        pre[i] = pre[i-1] + d[i-n];
        mpre[i] = mpre[i-1] + (d[i-n]*(d[i-n]+1))/2;
    }

    for(ll i=1;i<=n;++i){
        int idx = bs(i, x, pre, n);

        int p = idx;
        ll rest = x - (pre[idx] - pre[i-1]);
        if(x <= d[i]){
            ans = max(ans, (d[i]*(d[i]+1))/2 - ((d[i]-x)*(d[i]-x+1))/2);
            continue;
        }

        if(rest >= d[i-1]){
            ll sum = mpre[idx] - mpre[i-1] + (rest*(rest+1))/2;
            ans = max(ans, sum);
            return 0;
        }
        else{
            int p = bins(d[i-1]-rest, i, idx, pre);
            if(p!=-1){
                ll sum = mpre[p-1] - mpre[i-1] + (d[i-1]*(d[i-1]+1))/2 - ((d[i-1]-(rest+pre[idx]-pre[p-1]))*(d[i-1]-(rest+pre[idx]-pre[p-1])+1))/2;
                ans = max(sum, ans);
            }
            else{
                ll sum = mpre[idx] - mpre[i-1] + (d[i-1]*(d[i-1]+1))/2 - ((d[i-1]-rest)*(d[i-1]-rest+1))/2;
                ans = max(ans, sum);
            }


        }

    }
    cout<<ans;
    return 0;
}

int main(){
    fast;
    int t=1;
    //cin>>t;
    while(t--){
        solve();
    }

    return 0;
}