#include using namespace std; #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n)-1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define per2(i, l, r) for (int i = (r)-1; i >= (l); i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template using minheap = priority_queue, greater>; template using maxheap = priority_queue; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } int pct(int x) { return __builtin_popcount(x); } int pct(ll x) { return __builtin_popcountll(x); } int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template void reorder(vector &a, const vector &ord) { int n = a.size(); vector b(n); for (int i = 0; i < n; i++) b[i] = a[ord[i]]; swap(a, b); } template T floor(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? x / y : (x - y + 1) / y); } template T ceil(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? (x + y - 1) / y : x / y); } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); cerr << fixed << setprecision(15); } } io_setup; constexpr int inf = (1 << 30) - 1; constexpr ll INF = (1LL << 60) - 1; // constexpr int MOD = 1000000007; constexpr int MOD = 998244353; template struct Fast_Fourier_Transform { using comp = complex; static double pi; static vector r, ir; Fast_Fourier_Transform() {} static void init() { if (!r.empty()) return; r.resize(30), ir.resize(30); for (int i = 0; i < 30; i++) { r[i] = -polar(1.0, pi / (1 << (i + 1))); // r[i] := 1 の 2^(i+2) 乗根 ir[i] = -polar(1.0, -pi / (1 << (i + 1))); // ir[i] := 1/r[i] } } static vector to_comp(vector a) { vector ret(a.size()); for (int i = 0; i < (int)a.size(); i++) ret[i] = comp(a[i], 0.0); return ret; } static vector to_T(vector a) { vector ret(a.size(), 0); for (int i = 0; i < (int)a.size(); i++) ret[i] = a[i].real() + 0.1; // 整数の場合、誤差をケア // for(int i = 0; i < (int)a.size(); i++) ret[i] = a[i].real(); // 小数の場合 return ret; } static void fft(vector &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); for (int k = n; k >>= 1;) { comp w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { comp x = a[i], y = w * a[j]; a[i] = x + y, a[j] = x - y; } w *= r[__builtin_ctz(++t)]; } } } static void ifft(vector &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); a.resize(n); for (int k = 1; k < n; k <<= 1) { comp w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { comp x = a[i], y = a[j]; a[i] = x + y, a[j] = w * (x - y); } w *= ir[__builtin_ctz(++t)]; } } for (auto &e : a) e /= n; } static vector convolve(vector a, vector b) { int k = (int)a.size() + (int)b.size() - 1, n = 1; while (n < k) n <<= 1; vector A = to_comp(a), B = to_comp(b); A.resize(n), B.resize(n); fft(A), fft(B); for (int i = 0; i < n; i++) A[i] *= B[i]; ifft(A); vector c = to_T(A); c.resize(k); return c; } }; template double Fast_Fourier_Transform::pi = acos(-1.0); template vector> Fast_Fourier_Transform::r = vector>(); template vector> Fast_Fourier_Transform::ir = vector>(); using FFT = Fast_Fourier_Transform; struct Random_Number_Generator { mt19937_64 mt; Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {} int64_t operator()(int64_t l, int64_t r) { uniform_int_distribution dist(l, r - 1); return dist(mt); } int64_t operator()(int64_t r) { return (*this)(0, r); } } rng; using ull = unsigned long long; const ull mod = (1ULL << 61) - 1; ull hash_mod(ull x) { ull ret = (x >> 61) + (x & mod); return ret - (ret >= mod ? mod : 0); } ull hash_mul(ull x, ull y) { x = hash_mod(x), y = hash_mod(y); ull x1 = x >> 31, x2 = x & ((1ULL << 31) - 1), y1 = y >> 31, y2 = y & ((1ULL << 31) - 1); ull z = x1 * y2 + x2 * y1, z1 = z >> 30, z2 = z & ((1ULL << 30) - 1); return hash_mod(x1 * y1 * 2 + x2 * y2 + z1 + (z2 << 31)); } ull hash_pow(ull x, ull n) { ull ret = 1; for (; n > 0; n >>= 1, x = hash_mul(x, x)) { if (n & 1) ret = hash_mul(ret, x); } return ret; } // m 以上の base を乱択で生成する ull generate_base(ull m = (1ULL << 50)) { while (true) { ull k = rng(mod); if (gcd(mod - 1, k) != 1) continue; ull base = hash_pow(3, k); if (base >= m) return base; } return 0; } // 0 が含まれないように template struct Rolling_Hash { const int n; const ull base; // 基数 vector hashed, pw; Rolling_Hash(const T &s, ull base) : n(s.size()), base(base) { hashed.assign(n + 1, 0), pw.assign(n + 1, 1); for (int i = 0; i < n; i++) { pw[i + 1] = hash_mul(pw[i], base); hashed[i + 1] = hash_mul(hashed[i], base) + s[i]; if (hashed[i + 1] >= mod) hashed[i + 1] -= mod; } } // 文字列の [l,r) の部分のハッシュ値 ull get_hash(int l, int r) const { ull ret = hashed[r] + mod - hash_mul(hashed[l], pw[r - l]); return ret - (ret >= mod ? mod : 0); } ull get_all_hash() const { return hashed[n]; } // s[l1:r1] と s[l2:r2] の最長共通接頭辞 int lcp(int l1, int r1, int l2, int r2) { int ok = 0, ng = min(r1 - l1, r2 - l2) + 1; while (ng - ok > 1) { int mid = (ok + ng) / 2; (get_hash(l1, l1 + mid) == get_hash(l2, l2 + mid) ? ok : ng) = mid; } return ok; } // s[l1:r1] と s[l2:r2] の辞書順大小比較 (-1 : <, 0 : =, 1 : >) int comp(int l1, int r1, int l2, int r2) { int d = lcp(l1, r1, l2, r2); if (r1 == l1 + d && r2 == l2 + d) return 0; if (r1 == l1 + d) return -1; if (r2 == l2 + d) return 1; return get_hash(l1 + d, l1 + d + 1) < get_hash(l2 + d, l2 + d + 1) ? -1 : 1; } }; template struct Fixed_Size_Hash { const int n; const ull base; vector v; ull hashed; vector pw; Fixed_Size_Hash(const vector &v, ull base) : n(v.size()), base(base), v(v) { hashed = 0; pw.assign(n + 1, 1); for (int i = 0; i < n; i++) { pw[i + 1] = hash_mul(pw[i], base); hashed = hash_mul(hashed, base) + v[i]; if (hashed >= mod) hashed -= mod; } } Fixed_Size_Hash(int m, const T &x, ull base) : Fixed_Size_Hash(vector(m, x), base) {} ull add(int i, const T &x) { hashed += hash_mul(pw[n - 1 - i], mod + x); if (hashed >= mod) hashed -= mod; v[i] += x; return hashed; } ull change(int i, const T &x) { return add(i, x - v[i]); } ull get_hash() const { return hashed; } }; void solve() { int N, M, K; cin >> N >> M >> K; string S, T; cin >> S >> T; swap(S, T), swap(N, M); auto ch = [&](char c) { if (!islower(c)) return char(c + 'a' - 'A'); return c; }; vector a1(N, 0), b1(M, 0), a2(N, 0), b2(M, 0); rep(i, N) { if (islower(S[i])) { a1[i] = 1; } else { a2[i] = 1; } S[i] = ch(S[i]); } rep(i, M) { if (islower(T[i])) { b1[i] = 1; } else { b2[i] = 1; } T[i] = ch(T[i]); } ull base = generate_base(); Rolling_Hash rhs(S, base), rht(T, base); ull h = rhs.get_all_hash(); reverse(all(a1)), reverse(all(a2)); auto c1 = FFT::convolve(a1, b1); auto c2 = FFT::convolve(a2, b2); // print(a), print(b), print(c); int ans = 0; rep(i, M - N + 1) { if (rht.get_hash(i, i + N) == h) { int len = c1[i + N - 1] + c2[i + N - 1]; if (1 <= len && len <= K) ans++; } } cout << ans << '\n'; } int main() { int T = 1; // cin >> T; while (T--) solve(); }