#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};

// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = n;
  if (m >>= 1) {
    for (int i = 0; i < m; ++i) {
      const unsigned x = as[i + m].x;  // < MO
      as[i + m].x = as[i].x + MO - x;  // < 2 MO
      as[i].x += x;  // < 2 MO
    }
  }
  if (m >>= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned x = (prod * as[i + m]).x;  // < MO
        as[i + m].x = as[i].x + MO - x;  // < 3 MO
        as[i].x += x;  // < 3 MO
      }
      prod *= FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  for (; m; ) {
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i + m].x = as[i].x + MO - x;  // < 4 MO
          as[i].x += x;  // < 4 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
    if (m >>= 1) {
      Mint prod = 1U;
      for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
        for (int i = i0; i < i0 + m; ++i) {
          const unsigned x = (prod * as[i + m]).x;  // < MO
          as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
          as[i + m].x = as[i].x + MO - x;  // < 3 MO
          as[i].x += x;  // < 3 MO
        }
        prod *= FFT_RATIOS[__builtin_ctz(++h)];
      }
    }
  }
  for (int i = 0; i < n; ++i) {
    as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
    as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x;  // < MO
  }
}

// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
  assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
  int m = 1;
  if (m < n >> 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
    m <<= 1;
  }
  for (; m < n >> 1; m <<= 1) {
    Mint prod = 1U;
    for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
      for (int i = i0; i < i0 + (m >> 1); ++i) {
        const unsigned long long y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
        as[i].x += as[i + m].x;  // < 4 MO
        as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
        const unsigned long long y = as[i].x + MO - as[i + m].x;  // < 2 MO
        as[i].x += as[i + m].x;  // < 2 MO
        as[i + m].x = (prod.x * y) % MO;  // < MO
      }
      prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
    }
  }
  if (m < n) {
    for (int i = 0; i < m; ++i) {
      const unsigned y = as[i].x + MO2 - as[i + m].x;  // < 4 MO
      as[i].x += as[i + m].x;  // < 4 MO
      as[i + m].x = y;  // < 4 MO
    }
  }
  const Mint invN = Mint(n).inv();
  for (int i = 0; i < n; ++i) {
    as[i] *= invN;
  }
}

void fft(vector<Mint> &as) {
  fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
  invFft(as.data(), as.size());
}

vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
  if (as.empty() || bs.empty()) return {};
  const int len = as.size() + bs.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  bs.resize(n); fft(bs);
  for (int i = 0; i < n; ++i) as[i] *= bs[i];
  invFft(as);
  as.resize(len);
  return as;
}
vector<Mint> square(vector<Mint> as) {
  if (as.empty()) return {};
  const int len = as.size() + as.size() - 1;
  int n = 1;
  for (; n < len; n <<= 1) {}
  as.resize(n); fft(as);
  for (int i = 0; i < n; ++i) as[i] *= as[i];
  invFft(as);
  as.resize(len);
  return as;
}
////////////////////////////////////////////////////////////////////////////////


constexpr int MAX = 2010;
using Vec = bitset<MAX>;

Mint two[MAX], two2[MAX], qFac[MAX], qInvFac[MAX];
void qPrepare() {
  two[0] = two2[0] = qFac[0] = 1;
  for (int i = 1; i < MAX; ++i) {
    two[i] = two[i - 1] * 2;
    two2[i] = two2[i - 1] * two[i - 1];
    qFac[i] = qFac[i - 1] * (two[i] - 1);
  }
  qInvFac[MAX - 1] = qFac[MAX - 1].inv();
  for (int i = MAX; --i >= 1; ) {
    qInvFac[i - 1] = (two[i] - 1) * qInvFac[i];
  }
}
Mint qBinom(int n, int k) {
  assert(0 <= k); assert(k <= n);
  return qFac[n] * qInvFac[k] * qInvFac[n - k];
}

int N, M;
Vec B[MAX], X;

char buf[MAX];
void readVec(Vec &vec) {
  scanf("%s", buf);
  vec.reset();
  for (int j = 0; j < M; ++j) {
    vec[j] = buf[M - 1 - j] - '0';
  }
}

int main() {
  qPrepare();
  for (; ~scanf("%d%d", &N, &M); ) {
    for (int i = 0; i < N; ++i) {
      readVec(B[i]);
    }
    readVec(X);
    
    int r = 0;
    vector<int> js;
    for (int j = M; --j >= 0; ) {
      for (int i = r; i < N; ++i) if (B[i][j]) {
        swap(B[r], B[i]);
        break;
      }
      if (r < N && B[r][j]) {
        for (int i = 0; i < N; ++i) if (r != i && B[i][j]) {
          B[i] ^= B[r];
        }
        ++r;
        js.push_back(j);
      }
    }
// cerr<<"r = "<<r<<", js = "<<js<<endl;
// for(int i=0;i<N;++i){for(int j=M;--j>=0;)cerr<<B[i][j];cerr<<endl;}
    
    Mint ans = 0;
    if (r == N) {
      /*
        \oplus[i] B[N-1-i] c[i] <= X
        <=> \sum[i] 2^i c[i] < Y
      */
      vector<int> ys(N + 1, 0);
      {
        Vec x;
        for (int i = N; --i >= 0; ) {
          x ^= B[N - 1 - i];
          bool ok = true;
          for (int j = M; --j >= 0; ) {
            if (!x[j] && X[j]) { ok = true; break; }
            if (x[j] && !X[j]) { ok = false; break; }
          }
          if (ok) {
            ++ys[i];
          } else {
            x ^= B[N - 1 - i];
          }
        }
      }
      ++ys[0];
      for (int j = 0; j < N; ++j) {
        ys[j + 1] += ys[j] / 2;
        ys[j] %= 2;
      }
      int n = -1;
      for (int j = 0; j <= N; ++j) if (ys[j]) {
        n = j;
      }
// cerr<<"n = "<<n<<", ys = "<<ys<<endl;
      
      if (N <= n + 1) {
        /*
          Y = 10110
              1010*
              100**
              0****
        */
        // PIE
        vector<Mint> crt(n + 2, 0);
        crt[0] = 1;
        for (int i = 0; i <= n; ++i) if (ys[i]) {
          vector<Mint> nxt(n + 2, 0);
          
          // add nothing
          if (i < n) {
            for (int k = 0; k <= n + 1; ++k) {
              nxt[k] += crt[k];
            }
          }
          
          /*
            choose any (or i == n)
            low bits: k-dim -> l-dim
            count pairs (subspace, subset of vectors)
            nxt[l + ?] += \sum[k<=m<=l] coef(l, m) qbinom(i-k, m-k) way(m) crt[k + ?]
            subspace inversion:
                g[l] = \sum[0<=m<=l] qbinom(i-m, l-m) f[m]
                f[l] = \sum[0<=m<=l] (-1)^(l-m) 2^binom(l-m,2) qbinom(i-m, l-m) g[m]
            - i < n
                take one of 2^i vectors
                choose from (2^l-1) vectors
                remove multiple counting
                way(m) = 2^i \sum[a] (1/(a+1)) binom(2^m-1, a)
                       = 2^i (2^(2^m) - 1) / 2^m
            - i == n
                choose from (2^m-1) vectors
                way(m) = 2^(2^m-1)
          */
          // from zero space or from non-zero space
          for (int phase = 0; phase < 2; ++phase) {
            vector<Mint> fs(i + 1, 0), gs(i + 1, 0);
            if (phase == 0) {
              fs[0] += crt[0] * qFac[i - 0];
            } else {
              for (int k = 0; k <= i; ++k) {
                fs[k] = crt[k + 1] * qFac[i - k];
              }
            }
            for (int k = 0; k <= i; ++k) {
              gs[k] = qInvFac[k];
            }
            fs = convolve(fs, gs);
            fs.resize(i + 1);
            Mint t = 1;
            for (int k = 0; k <= i; ++k) {
              fs[k] *= ((i < n) ? (two[i - k] * (t * 2 - 1)) : t);
              t = t * t * 2;
              gs[k] = ((k&1)?-1:+1) * two2[k] * qInvFac[k];
            }
            fs = convolve(fs, gs);
            fs.resize(i + 1);
            for (int k = 0; k <= i; ++k) {
              nxt[k + phase + ((i < n) ? 1 : 0)] += fs[k] * qInvFac[i - k];
            }
// cerr<<"i = "<<i<<", nxt = "<<nxt<<endl;
          }
          
          swap(crt, nxt);
        }
// Mint all=0;for(int k=0;k<=N;++k)all+=crt[k];cerr<<"all = "<<all<<endl;
        
        ans += crt[N];
      }
    }
    printf("%u\n", ans.x);
  }
  return 0;
}