#include <bits/stdc++.h>
#define whlie while
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define rep(i,N) for(int i = 0; i < (N); i++)
#define repr(i,N) for(int i = (N) - 1; i >= 0; i--)
#define rep1(i,N) for(int i = 1; i <= (N) ; i++)
#define repr1(i,N) for(int i = (N) ; i > 0 ; i--)
#define each(x,v) for(auto& x : v)
#define all(v) (v).begin(),(v).end()
#define sz(v) ((int)(v).size())
#define ini(...) int __VA_ARGS__; in(__VA_ARGS__)
#define inl(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define ins(...) string __VA_ARGS__; in(__VA_ARGS__)
using namespace std; void solve();
using ll = long long; using vl = vector<ll>;
using vi = vector<int>; using vvi = vector< vector<int> >;
constexpr int inf = 1001001001;
constexpr ll infLL = (1LL << 61) - 1;
struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya;
template<typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template<typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T, typename U> ostream& operator <<(ostream& os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; }
template<typename T, typename U> istream& operator >>(istream& is, pair<T, U> &p) { is >> p.first >> p.second; return is; }
template<typename T> ostream& operator <<(ostream& os, const vector<T> &v) { int s = (int)v.size(); rep(i,s) os << (i ? " " : "") << v[i]; return os; }
template<typename T> istream& operator >>(istream& is, vector<T> &v) { for(auto &x : v) is >> x; return is; }
void in(){} template <typename T,class... U> void in(T &t,U &...u){ cin >> t; in(u...);}
void out(){cout << "\n";} template <typename T,class... U> void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);}
template<typename T>void die(T x){out(x); exit(0);}
#ifdef NyaanDebug
  #include "NyaanDebug.h"
  #define trc(...) do { cerr << #__VA_ARGS__ << " = "; dbg_out(__VA_ARGS__);} while(0)
  #define trca(v,N) do { cerr << #v << " = "; array_out(v , N);cout << endl;} while(0)
#else
  #define trc(...)
  #define trca(...)
  int main(){solve();}
#endif
using P = pair<int,int>; using vp = vector<P>;
constexpr int MOD = /** 1000000007; //*/ 998244353;
//////////


// verify
// https://atcoder.jp/contests/agc038/submissions/7683063
// https://www.codechef.com/viewsolution/26767783
struct multiple_transform{
  template <typename T>
  static constexpr void zeta_transform(vector<T> &a){
    int N = a.size() - 1;
    vector<int> sieve(N + 1, true);
    for(int p = 2; p <= N; ++p)
      if(sieve[p])
        for(int k = N / p; k > 0; --k)
          sieve[k * p] = false , a[k] += a[k * p];
  }
  template <typename T>
  static constexpr void mobius_transform(vector<T> &a){
    int N = a.size() - 1;
    vector<int> sieve(N + 1, true);
    for(int p = 2; p <= N; ++p)
      if(sieve[p])
        for(int k = 1; k * p <= N; ++k)
          sieve[k * p] = false , a[k] -= a[k * p];
  }

  template<typename T>
  static constexpr void zeta_transform(map<long long, T> &a){
    for(auto it=a.rbegin(); it!=a.rend(); it++)
      for(auto it2=a.rbegin(); it2!=it; it2++)
        if(it2->first % it->first == 0)
          it->second += it2->second;
  }
  template<typename T>
  static constexpr void mobius_transform(map<long long, T> &a){
    for(auto it=a.rbegin(); it!=a.rend(); it++)
      for(auto it2=a.rbegin(); it2!=it; it2++)
        if(it2->first % it->first == 0)
          it->second -= it2->second;
  }

};

template<int wsize>
struct F2 : bitset<wsize>{

  F2() : bitset<wsize>(){}
  F2(unsigned long long n) : bitset<wsize>(n){}
  F2(const string& s) : bitset<wsize>(s){}

  const int msb() const{
    for(int ret = wsize - 1 ; ret >= 0 ; ret-- )
      if( (*this)[ret] == 1 ) return ret;
    return -1;
  }

  const bool operator<(const F2<wsize> &other) const{
    for(int i = wsize - 1 ; i >= 0 ; i-- )
      if( (*this)[i] != other[i] ) return other[i];
    return true;
  }
};
template<int wsize>
F2<wsize> gcd(F2<wsize> x , F2<wsize> y){
  if(x < y) swap(x , y);
  while(!y.none()){
    int xm = x.msb() , ym = y.msb();
    x ^= y << (xm - ym);
    if(x < y) swap(x , y);
  }
  return x;
}

using f2 = F2<4096>;

void solve(){
  ini(N); ins(x);
  vector<string> v(N); in(v);
  f2 g;
  rep(i , N) g = gcd(g , f2(v[i]));

  f2 X(x);

  if(X.msb() < g.msb()) die(0);
  // d次の項だけで判定
  ll ans = 0;
  for(int i = X.msb(); i >= g.msb(); i--){
    ans *= 2;
    ans += (X[i] == 1);
    if(ans >= MOD) ans %= MOD;
  }
  ans = (ans + 1) % MOD;
  // 並んでいるときは？
  f2 Y = X;
  rep(i , g.msb() ) Y[i] = 0;

  for(int i = Y.msb(); i >= g.msb() ; i--){
    if(Y[i]) Y ^= g << ( i - g.msb() );
  }

  for(int i = g.msb() - 1 ; i >= 0 ; i--){
    if(X[i] > Y[i]) break;
    if(Y[i] > X[i]) {ans =(ans + MOD - 1) % MOD; break;}
  }

  out(ans);




}

Measured memory_bytes: 256