#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
typedef long long int ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<vvvl> vvvvl;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<vvb> vvvb;
typedef vector<vvvb> vvvvb;
typedef pair<ll,ll> pl;
typedef pair<ll,pl> ppl;
typedef pair<ll,ppl> pppl;
typedef pair<ll,pppl> pppppl;
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(a) begin(a),end(a)
#define sz(a) (int)(a).size()
#define F first
#define S second
#define bs(A,x) binary_search(all(A),x)
#define lb(A,x) (ll)(lower_bound(all(A),x)-A.begin())
#define ub(A,x) (ll)(upper_bound(all(A),x)-A.begin())
#define cou(A,x) (ll)(upper_bound(all(A),x)-lower_bound(all(A),x))
template<typename T>using min_priority_queue=priority_queue<T,vector<T>,greater<T>>;
template<class T>bool chmax(T&a,T b){if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T&a,T b){if(b<a){a=b;return 1;}return 0;}
/*
using mint=modint998244353;
const ll mod=998244353;
//*/
//*
using mint=modint1000000007;
const ll mod=1000000007;
//*/
//using mint=modint;
//*
typedef vector<mint> vm;
typedef vector<vm> vvm;
typedef vector<vvm> vvvm;
typedef vector<vvvm> vvvvm;
ostream&operator<<(ostream&os,mint a){os<<a.val();return os;}
istream&operator>>(istream&is,mint&a){int x;is>>x;a=mint(x);return is;}
//*/
template<typename T1,typename T2>ostream&operator<<(ostream&os,pair<T1,T2>p){os<<p.F<<" "<<p.S;return os;}
template<typename T1,typename T2>istream&operator>>(istream&is,pair<T1,T2>&p){is>>p.F>>p.S;return is;}
template<typename T>ostream&operator<<(ostream&os,vector<T>v){rep(i,0,sz(v))os<<v[i]<<(i+1!=sz(v)?" ":"");return os;}
template<typename T>istream&operator>>(istream&is,vector<T>&v){for(T&in:v)is>>in;return is;}
int main(){
  cin.tie(0)->sync_with_stdio(0);
  cin.exceptions(cin.failbit);
  
  string S;ll K;cin>>S>>K;
  ll N=sz(S);
  vvm X(3,vm(3)),Y(3,vm(3)),Z(3,vm(3));
  X[0][0]=X[1][1]=1;
  rep(i,0,N){
  	vvm _X=X,_Y=Y,_Z=Z;
  	if(S[i]=='0'){
  		_X[0][0]+=X[0][1];_X[1][0]+=X[1][1];
  		_Y[0][0]+=Y[0][1]+X[0][1];_Y[1][0]+=Y[1][1]+X[1][1];
  		_Z[0][0]+=Z[0][1]+2*Y[0][1]+X[0][1];_Z[1][0]+=Z[1][1]+2*Y[1][1]+X[1][1];
  	}
  	else{
  		_X[0][1]+=X[0][0];_X[1][1]+=X[1][0];
  		_Y[0][1]+=Y[0][0]+X[0][0];_Y[1][1]+=Y[1][0]+X[1][0];
  		_Z[0][1]+=Z[0][0]+2*Y[0][0]+X[0][0];_Z[1][1]+=Z[1][0]+2*Y[1][0]+X[1][0];
  	}
  	X=_X;Y=_Y;Z=_Z;
  }
  X[2][0]=X[0][0]+X[1][0]-1;
  X[2][1]=X[0][1]+X[1][1]-1;
  X[2][2]=1;
  Y[2][0]=Y[0][0]+Y[1][0];
  Y[2][1]=Y[0][1]+Y[1][1];
  Z[2][0]=Z[0][0]+Z[1][0];
  Z[2][1]=Z[0][1]+Z[1][1];
  
  vvvvm dou(3,vvvm(60,vvm(3,vm(3))));
  dou[0][0]=X;dou[1][0]=Y;dou[2][0]=Z;
  rep(j,1,60){
  	rep(x,0,3)rep(y,0,3)rep(z,0,3){
  		dou[0][j][x][z]+=dou[0][j-1][x][y]*dou[0][j-1][y][z];
  		dou[1][j][x][z]+=dou[1][j-1][x][y]*dou[0][j-1][y][z]+dou[0][j-1][x][y]*dou[1][j-1][y][z];
  		dou[2][j][x][z]+=dou[2][j-1][x][y]*dou[0][j-1][y][z]+2*dou[1][j-1][x][y]*dou[1][j-1][y][z]+dou[0][j-1][x][y]*dou[2][j-1][y][z];
  	}
  }
  
  vvm DP(3,vm(3));
  DP[0][2]=1;
  rep(i,0,60)if((K>>i)%2){
  	vvm EP(3,vm(3));
  	rep(x,0,3)rep(y,0,3){
  		EP[0][y]+=DP[0][x]*dou[0][i][x][y];
  		EP[1][y]+=DP[0][x]*dou[1][i][x][y]+DP[1][x]*dou[0][i][x][y];
  		EP[2][y]+=DP[0][x]*dou[2][i][x][y]+2*DP[1][x]*dou[1][i][x][y]+DP[2][x]*dou[0][i][x][y];
  	}
  	DP=EP;
  }
  cout<<(DP[2][0]+DP[2][1]).val()<<endl;
  return 0;
}