#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;

template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

const int m=40;

signed main(){
    int n;ll k;cin>>n>>k;
    string s;cin>>s;

    vector<vector<ll>> p(n,vector<ll>(m+1,0)),b(n,vector<ll>(m+1,0));
    vector<vector<int>> to(n,vector<int>(m+1,0));
    rep(i,n){
        b[i][0]=1;
        p[i][0]=s[i]-'0';
        to[i][0]=(i+1)%n;
    }

    auto merge=[&](ll p_l,ll p_r,ll b_l,ll b_r){
        auto p_m=p_r+max(0ll,p_l-b_r);
        auto b_m=b_l+max(0ll,b_r-p_l);
        return make_pair(p_m,b_m);
    };

    for(int j=0;j<m;j++){
        rep(i,n){
            to[i][j+1]=to[to[i][j]][j];
            ll p_l=p[i][j],p_r=p[to[i][j]][j];
            ll b_l=b[i][j],b_r=b[to[i][j]][j];
            tie(p[i][j+1],b[i][j+1])=merge(p_l,p_r,b_l,b_r);
        }
    }
    ll P=0,B=0;
    int cur=0;
    for(int i=0;i<=m;i++){
        if((k>>i)&1){
            tie(P,B)=merge(P,p[cur][i],B,b[cur][i]);
            cur=to[cur][i];
        }
    }
    cout<<B<<endl;
    return 0;
}