#include #include #include #include #include #define FOR(i,k,n) for(int i = (k);i < (n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(x) begin(x),end(x) using namespace std; using vecint = vector; using ll = int64_t; using vecll = vector; using P = complex; const double pi = acos(-1.0); vector

FFT(double theta, const vector

&a) { const int n = a.size(); vector

ret = a; for (int m = n; m >= 2; m >>= 1, theta *= 2) { REP(i,m/2) { for (int j = i; j < n; j += m) { int k = j + m / 2; P x = ret[j] - ret[k]; ret[j] += ret[k]; ret[k] = exp(i * theta * P(0, 1)) * x; } } } for (int i = 0, j = 1; j < n - 1; j++) { for (int k = n >> 1; k > (i ^= k); k >>= 1) {;} if (j < i) swap(ret[i], ret[j]); } return ret; } vector convolution(const vector &lhs, const vector &rhs) { int n = 1, a = lhs.size(), b = rhs.size(); while (n < max(a, b) * 2) n <<= 1; vector

temp1(n), temp2(n); REP(i,n/2) { if (i < a) temp1[i] = P(lhs[i], 0); if (i < b) temp2[i] = P(rhs[i], 0); } temp1 = FFT(2.0 * pi / n, temp1); temp2 = FFT(2.0 * pi / n, temp2); REP(i,n) temp1[i] *= temp2[i]; temp1 = FFT(-2.0 * pi / n, temp1); vector ret(n); REP(i,n) ret[i] = temp1[i].real() / n + 0.5; return ret; } constexpr ll MOD = 998244353; constexpr ll MAX_F = 600000; // a^-1 mod p ll inv(ll a,ll p){ return ( a == 1 ? 1 : (1 - p*inv(p%a,a)) / a + p ); } int main() { vecll fact(MAX_F+1), finv(MAX_F+1); fact[0] = 1; REP(i,MAX_F) { fact[i+1] = fact[i] * (i+1) % MOD; } finv[MAX_F] = inv(fact[MAX_F], MOD); REP(ri,MAX_F) { int i = MAX_F - ri; finv[i-1] = finv[i] * i % MOD; } auto comb = [&] (ll n, ll k) { return fact[n] * finv[k] % MOD * finv[n-k] % MOD; }; ll n,k; cin>>n>>k; string s; cin>>s; vecll left_i(n, 0), right_n(n, 0); REP(i,n) { if (s[i] == 'i') { left_i[i] = 1; } else { right_n[n-1-i] = 1; } } auto poly = convolution(left_i, right_n); ll ans = 0; REP(i,n-k-1) { ll span = n-2-i; ans += poly[i] * comb(span,k) % MOD; ans %= MOD; } cout<