#include #define FOR(i, n, m) for(ll i = (n); i < (ll)(m); i++) #define REP(i, n) FOR(i, 0, n) #define ALL(v) v.begin(), v.end() #define pb push_back using namespace std; using ll = long long; using ld = long double; using P = pair; constexpr ll inf = 1000000000; constexpr ll mod = 998244353; constexpr long double eps = 1e-6; template ostream& operator<<(ostream& os, pair p) { os << to_string(p.first) << " " << to_string(p.second); return os; } template ostream& operator<<(ostream& os, vector& v) { REP(i, v.size()) { if(i) os << " "; os << v[i]; } return os; } struct modint { ll n; public: modint(const ll n = 0) : n((n % mod + mod) % mod) {} static modint pow(modint a, int m) { modint r = 1; while(m > 0) { if(m & 1) { r *= a; } a = (a * a); m /= 2; } return r; } modint &operator++() { *this += 1; return *this; } modint &operator--() { *this -= 1; return *this; } modint operator++(int) { modint ret = *this; *this += 1; return ret; } modint operator--(int) { modint ret = *this; *this -= 1; return ret; } modint operator~() const { return (this -> pow(n, mod - 2)); } // inverse friend bool operator==(const modint& lhs, const modint& rhs) { return lhs.n == rhs.n; } friend bool operator<(const modint& lhs, const modint& rhs) { return lhs.n < rhs.n; } friend bool operator>(const modint& lhs, const modint& rhs) { return lhs.n > rhs.n; } friend modint &operator+=(modint& lhs, const modint& rhs) { lhs.n += rhs.n; if (lhs.n >= mod) lhs.n -= mod; return lhs; } friend modint &operator-=(modint& lhs, const modint& rhs) { lhs.n -= rhs.n; if (lhs.n < 0) lhs.n += mod; return lhs; } friend modint &operator*=(modint& lhs, const modint& rhs) { lhs.n = (lhs.n * rhs.n) % mod; return lhs; } friend modint &operator/=(modint& lhs, const modint& rhs) { lhs.n = (lhs.n * (~rhs).n) % mod; return lhs; } friend modint operator+(const modint& lhs, const modint& rhs) { return modint(lhs.n + rhs.n); } friend modint operator-(const modint& lhs, const modint& rhs) { return modint(lhs.n - rhs.n); } friend modint operator*(const modint& lhs, const modint& rhs) { return modint(lhs.n * rhs.n); } friend modint operator/(const modint& lhs, const modint& rhs) { return modint(lhs.n * (~rhs).n); } }; istream& operator>>(istream& is, modint m) { is >> m.n; return is; } ostream& operator<<(ostream& os, modint m) { os << m.n; return os; } using mi = modint; ll mod_pow(__int128 a, __int128 n, __int128 m = mod) { using ll = __int128; ll ret = 1; ll tmp = a; while(n > 0) { if(n % 2) ret *= tmp; ret %= m; tmp = tmp * tmp; tmp %= m; n /= 2; } return ret % m; } constexpr int MAX_N = 2020202; mi mod_fact [MAX_N + 1]; mi mod_fact_i[MAX_N + 1]; mi mod_comb(long long n, long long k) { static bool initialized = false; if(n < 0 || k < 0 || n < k) return 0; if(not initialized) { mod_fact[0] = 1; for(int i = 1; i <= MAX_N; ++i) { mod_fact[i] = i * mod_fact[i - 1]; } mod_fact_i[MAX_N] = mod_pow(mod_fact[MAX_N].n, mod - 2); for(int i = MAX_N - 1; i >= 0; --i) { mod_fact_i[i] = mod_fact_i[i + 1] * (i + 1); } initialized = true; } return mod_fact[n] * mod_fact_i[n - k] * mod_fact_i[k]; } struct union_find { union_find(int n) : par_(n, -1) {} void init(int n) { par_.assign(n, -1); } int root(int x) { return par_[x] < 0 ? x : par_[x] = root(par_[x]); } bool unite(int x, int y) { x = root(x); y = root(y); if(x == y) return false; if(par_[x] < par_[y]) { par_[x] += par_[y]; par_[y] = x; } else { par_[y] += par_[x]; par_[x] = y; } return true; } bool same(int x, int y) { return root(x) == root(y); } int size(int x) { return -par_[root(x)]; } vector par_; }; ll gcd(ll a, ll b) { if (b == 0) return a; return gcd(b, a % b); } ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g * b; } ll N = 202020; ll bit[202020]; void add(ll a, ll w) { a++; for (ll x = a; x <= N; x += x & -x) bit[x] += w; } ll sum(ll a) { a++; ll ret = 0; for (ll x = a; x > 0; x -= x & -x) ret += bit[x]; return ret; } // return the sum of [a, b) ll sum(ll a, ll b) { ll ret = 0; if(b == 0) return 0; ret += sum(b - 1); if(a) ret -= sum(a - 1); return ret; } int n, m, k; string x; void flip() { REP(i, m) { if(x[i] == '0') x[i] = '1'; else x[i] = '0'; } } vector> memo; mi dfs(int rem_digit, int rem_pos) { if(rem_digit == 0 || rem_pos == 0) return 1; if(memo[rem_digit][rem_pos].n != -1) return memo[rem_digit][rem_pos]; if(x[m - rem_digit] == '0') { mi sum = 0; for(int i = 0; i < k; i++) sum += mod_comb(rem_pos, i); return memo[rem_digit][rem_pos] = sum * dfs(rem_digit - 1, rem_pos); } else { mi ret = 0; for(int i = 0; i <= rem_pos; i++) { ret += mod_comb(rem_pos, i) * dfs(rem_digit - 1, i) * mod_pow(2, (rem_pos - i) * (rem_digit - 1)); } return memo[rem_digit][rem_pos] = ret; } } mi solve(bool debug) { flip(); memo.clear(); memo.resize(m + 1); REP(i, m + 1) memo[i].resize(n + 1); REP(i, m + 1) REP(j, n + 1) memo[i][j].n = -1; mi ans = dfs(m, n); REP(i, m + 1) REP(j, n + 1) { if(debug) cout << i << " " << j << " " << dfs(i, j) << endl; } flip(); return ans; } int main() { cin.tie(0); ios::sync_with_stdio(false); cin >> n >> m >> k >> x; bool cont0 = false; REP(i, m) if(x[i] == '0') cont0 = true; mi ans = solve(false); //cout << ans << endl; if(cont0) { for(int i = m - 1; i >= 0; i--) { if(x[i] == '1') continue; x[i] = '1'; for(int j = i + 1; j < m; j++) { x[j] = '0'; } break; } ans -= solve(false); } cout << ans << endl; return 0; }