#include <string>
#include<bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> indexed_set;
//#pragma GCC target("avx2")
//order_of_key #of elements less than x
// find_by_order kth element
using ll=long long;
using ld=long double;
using pii=pair<int,int>;
#define f first
#define s second
#define pb push_back
#define REP(i,n) for(int i=0;i<n;i++)
#define REP1(i,n) for(int i=1;i<=n;i++)
#define FILL(n,x) memset(n,x,sizeof(n))
#define ALL(_a) _a.begin(),_a.end()
#define sz(x) (int)x.size()
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()),c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
//you may define some global variables, but it does not work if you try to transfer any information from function pigeon_num or function send to function receive through these variables.
//you had better not use the same global variables in function send and in function receive.

/*
Taskid:         The index of the subtask. If it is subtask 2, then Taskid=2.
k:              The time threshold. Suppose the i-th pigeon taking off is the p_i-th one to land. It is guaranteed that abs(i-p_i)<=k.
return value:   The number of pigeons Little E will use.
*/
int pigeon_num(int Taskid, int k){
	return (k+1)*128-k;
}

/*
Taskid:         The index of the subtask. If it is subtask 2, then Taskid=2.
n:              The number of pigeons Little E will use. This equals the return value of function pigeon_num.
k:              The time threshold. Suppose the i-th pigeon taking off is the p_i-th one to land. It is guaranteed that abs(i-p_i)<=k.
msg:            The content of the message.
return value:	The order of the pigeons taking off. The length of this string must be n. return_value[i]='0' means the (i+1)-th pigeon taking off is black. return_value[i]='1' means the (i+1)-th pigeon taking off is white.
*/
std::string send(int Taskid, int n, int k, __uint128_t msg){
	string ans="";
	REP(i,128){
		int z=msg%2;
		REP(j,k+1) ans.pb(z+'0'); 
		msg/=2;
	}
	reverse(ALL(ans));
	REP(j,k) ans.pop_back();
	return ans;
}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

class Init{
public:
	Init(){
		//you may do some initialization for RECEIVE function here
	}
};

/*
Taskid:         The index of the subtask. If it is subtask 2, then Taskid=2.
k:              The time threshold. Suppose the i-th pigeon taking off is the p_i-th one to land. It is guaranteed that abs(i-p_i)<=k.
msg:			The order of the pigeons landing. Its length is equal to n. msg[i] denotes the color of the (i+1)-th pigeon watched landing by Little F. '0' means black and '1' means white.
return value:	The content of the message. It should be correct.
*/
__uint128_t receive(int Taskid, int k, const std::string &msg){

	const static Init init;
	int n=sz(msg);
	__uint128_t ans=0;
	vector<int> s[2];
	REP(i,n) s[msg[i]-'0'].pb(i);
	REP(a,k+1) s[0].pb(n+a),s[1].pb(n+a);
	REP(j,2) reverse(ALL(s[j]));
	REP(i,128){
		int z=min(s[0].back(),s[1].back());
		int p=(s[1].back()==z);
		ans=ans*2+p;
		REP(j,k+1) s[p].pop_back();
	}
	return ans;
}