#include <stdio.h>
#include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
using namespace atcoder;
using mint = modint1000000007;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf32 1000000005
#define Inf64 1000000000000000001LL
vector<vector<vector<mint>>> merge(const vector<vector<vector<mint>>>& a, const vector<vector<vector<mint>>>& b) {
	vector res(2,vector(2,vector<mint>(3,0)));
	rep(i,2){
		rep(j,2){
			rep(k,3){
				res[i][j][k] += a[i][j][k];
				res[i][j][k] += b[i][j][k];
			}
		}
	}
	rep(i,2){
		rep(j,2){
			rep(k,2){
				rep(l,3){
					rep(m,3){
						if(l+m>2)continue;
						mint v = 1;
						if(l==1 && m==1)v = mint(2).inv();
						res[i][k][l+m] += a[i][j][l] * b[j^1][k][m] * v;
					}
				}
			}
		}
	}
	return res;
}
int main(){
	
	string s;
	cin>>s;
	
	vector dp(2,vector(2,vector<mint>(3,0)));
	rep(i,s.size()){
		vector ndp(2,vector(2,vector<mint>(3,0)));
		ndp[s[i]-'0'][s[i]-'0'][0]++;
		ndp[s[i]-'0'][s[i]-'0'][1]+=2;
		ndp[s[i]-'0'][s[i]-'0'][2]++;
		rep(j,2){
			rep(k,2){
				rep(l,3){
					rep(ll,3){
						if(ll<l)continue;
						if(k!=s[i]-'0'){
							mint v = 1;
							if(l==0 && ll==1)v = 2;
							ndp[j][k^1][ll] += dp[j][k][l] * v;
						}
					}
					ndp[j][k][l] += dp[j][k][l];
					
				}
			}
		}
		swap(dp,ndp);
	}
	auto ans = dp;
	long long K;
	cin>>K;
	K--;
	rep(i,60){
		if((K>>i)&1){
			ans = merge(ans,dp);
		}
		dp = merge(dp,dp);
	}
	mint ansa = 0;
	rep(i,2){
		rep(j,2){
			ansa +=ans[i][j][2];
		}
	}
	cout<<ansa.val()<<endl;
	return 0;
}