#pragma region Tmpl #include // clang-format off #define pb push_back #define eb emplace_back #define fi first #define se second #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(...) long long __VA_ARGS__; in(__VA_ARGS__) #define ins(...) string __VA_ARGS__; in(__VA_ARGS__) #define inc(...) char __VA_ARGS__; in(__VA_ARGS__) #define in2(s,t) rep(i,sz(s)){in(s[i] , t[i]);} #define in3(s,t,u) rep(i,sz(s)){in(s[i] , t[i] , u[i]);} #define in4(s,t,u,v) rep(i,sz(s)){in(s[i] , t[i] , u[i] , v[i]);} #ifdef ONLINE_JUDGE #define rep(i,N) for(int i = 0; i < (int)(N); i++) #define repr(i,N) for(int i = (int)(N) - 1; i >= 0; i--) #define rep1(i,N) for(int i = 1; i <= (int)(N) ; i++) #define repr1(i,N) for(int i = (N) ; (int)(i) > 0 ; i--) #else #define rep(i,N) for(long long i = 0; i < (long long)(N); i++) #define repr(i,N) for(long long i = (long long)(N) - 1; i >= 0; i--) #define rep1(i,N) for(long long i = 1; i <= (long long)(N) ; i++) #define repr1(i,N) for(long long i = (N) ; (long long)(i) > 0 ; i--) #endif using namespace std; void solve(); using ll = long long; template using V = vector; using vi = V; using vl = V<>; using vvi = V< V >; using vd = V; using vs = V; using vvl = V< V<> >; constexpr int inf = 1001001001; constexpr ll infLL = (1LL << 61) - 1; template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } templatell ceil(T a,U b){return (a + b - 1) / b;} template ostream& operator <<(ostream& os, const pair &p) { os << p.first << " " << p.second; return os; } template istream& operator >>(istream& is, pair &p) { is >> p.first >> p.second; return is; } template ostream& operator <<(ostream& os, const vector &v) { int s = (int)v.size(); for(int i=0;i istream& operator >>(istream& is, vector &v) { for(auto &x : v) is >> x; return is; } void in(){} template void in(T &t,U &...u){ cin >> t; in(u...);} void out(){cout << "\n";} template void out(const T &t,const U &...u){ cout << t; if(sizeof...(u)) cout << " "; out(u...);} templatevoid 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);} while(0) #define trcc(v) do { cerr << "name : " << #v << "\n"; int cnt = 0; each(x , v){cerr << (cnt++) << " : "; trc(x); } } while(0) #else #define trc(...) #define trca(...) #define trcc(...) int main(){solve();} #endif constexpr ll TEN(int n){ll ret=1,x=10;while(n){if(n&1)ret*=x;x*=x;n>>=1;}return ret;} #define mem(a, val) memset(a, val, sizeof(a)) #pragma endregion struct IoSetupNya {IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7);} } iosetupnya; using P = pair; using vp = V

; constexpr uint32_t MOD = /** 1000000007; //*/ 998244353; // clang-format on //////////////////////////////////////////////////// // Suffix Array //verify https://judge.yosupo.jp/submission/240 struct SuffixArray{ int _size; vector sa; string &s; SuffixArray(string &str):_size(str.size()) , s(str) { // うしさんのO( N logN )の実装 s.push_back(0); sa.resize(s.size()); iota(begin(sa), end(sa), 0); sort(begin(sa), end(sa), [&](int a, int b) { return s[a] == s[b] ? a > b : s[a] < s[b]; }); vector< int > classes(s.size()), c(s.begin(), s.end()), cnt(s.size()); for(int len = 1; len < (int)s.size(); len <<= 1) { for(int i = 0; i < (int)s.size(); i++) { if(i > 0 && c[sa[i - 1]] == c[sa[i]] && sa[i - 1] + len < (int)s.size() && c[sa[i - 1] + len / 2] == c[sa[i] + len / 2]) { classes[sa[i]] = classes[sa[i - 1]]; } else { classes[sa[i]] = i; } } iota(begin(cnt), end(cnt), 0); copy(begin(sa), end(sa), begin(c)); for(int i = 0; i < (int)s.size(); i++) { int s1 = c[i] - len; if(s1 >= 0) sa[cnt[classes[s1]]++] = s1; } classes.swap(c); } s.pop_back(); } // デバッグ用に実装 void output() { cout << "SA\tidx\tstr" << endl; for(int i = 0; i < size(); i++) { cout << i << ": \t" << sa[i] << " \t" ; if(sa[i] != _size) cout << s.substr(sa[i],_size - sa[i]) << endl; else cout << "$" << endl; } cout << endl; } // sa.size()と表せると便利なので実装 int size() const{return _size + 1;} // sa[]と表せると便利なのでオーバーロードしておく int operator[](int k) const{return sa[k]; } }; struct LCPArray { const SuffixArray &SA; vector LCP, rank; LCPArray(const SuffixArray &sa) : SA(sa) { LCP.resize(SA.size()); rank.resize(SA.size()); // 初期化 rankはsaの逆関数 for(int i = 0; i < SA.size(); i++) { rank[SA[i]] = i; } LCP[0] = 0; // 構築 for(int i = 0, h = 0; i < SA.size() - 1 ; i++) { int j = SA[rank[i] - 1] ; h ? h-- : h; // ここで尺取り法に近い手法を使うことでO(N)でLCPの構築をしている while( (i > j ? i : j) + h < SA.size() - 1 && SA.s[i + h] == SA.s[j + h] && ++h ); LCP[rank[i] - 1] = h; } } // デバッグ用に実装 void output() { cout << "SA\tidx\tLCP\tstr" << endl; for(int i = 0 ; i < SA.size() ; i++){ cout << i << "\t" << SA[i] <<" \t" << LCP[i] << "\t"; if(SA[i] == SA.size() - 1) cout << "$"; else cout << SA.s.substr(SA[i] , SA.size() - 1 - SA[i]); cout << endl; } } }; // Sparse Table template struct SparseTable{ vector< vector< T > > table; vector< int > log_table; SparseTable(const vector< T > &v) { int b = 0; while((1 << b) <= (int)v.size()) ++b; table.assign(b, vector< T >(1 << b)); for(int i = 0; i < (int)v.size(); i++) { table[0][i] = v[i]; } for(int i = 1; i < b; i++) { for(int j = 0; j + (1 << i) <= (1 << b); j++) { table[i][j] = min(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]); } } log_table.resize(v.size() + 1); for(int i = 2; i < (int)log_table.size(); i++) { log_table[i] = log_table[i >> 1] + 1; } } // 区間 [l , r) の最小値を返す inline T query(int l, int r) { int b = log_table[r - l]; return min(table[b][l], table[b][r - (1 << b)]); } }; // 文字列検索 検索 O(M + logN) メモリO(N logN) // verify // https://onlinejudge.u-aizu.ac.jp/status/users/NyaanNyaan/submissions/1/ALDS1_14_D/judge/3874273/C++14 // https://atcoder.jp/contests/abc135/submissions/7574225 // https://judge.yosupo.jp/submission/241 // https://atcoder.jp/contests/abc141/submissions/7577295 struct StringSearch{ string &s; const SuffixArray &sa; const LCPArray &lcp; SparseTable sparse; StringSearch(LCPArray &lcp) : s(lcp.SA.s) , sa(lcp.SA) , lcp(lcp) , sparse(lcp.LCP){ } // 文字列sの[i , N)と[j , N)の共通接頭辞の長さを求める int ArbitaryLCP(int i , int j){ if(i == j) return (int)(s.size()) - i; return sparse.query( min(lcp.rank[i] , lcp.rank[j]) , max(lcp.rank[i] , lcp.rank[j]) ); } pair comp(const string &t , int len , int si , int ti = 0){ int sn = (int)s.size() , tn = (int) t.size(); si += len , ti += len; while(si < sn && ti < tn){ if(s[si] != t[ti]) return make_pair( s[si]=sn && ti find_range(int left , int med , int right , int len){ { int ng = left - 1, ok = med; while(ng + 1 < ok){ int cur = (ng + ok) / 2; if(sparse.query(cur , med) >= len) ok = cur; else ng = cur; } left = ok; } { int ok = med , ng = right + 1; while(ok + 1 < ng){ int cur = (ng + ok) / 2; if(sparse.query(med, cur) >= len) ok = cur; else ng = cur; } right = ok; } return make_pair(left , right); } // 全ての出現範囲をSA上の[left , right]の範囲で返す // 存在しない場合は-1を返す pair find(string &t){ // 条件を満たす[left , right]を見つける // sa[0]は空文字列なので left = 1 とする // lenは既に一致している文字列の長さ int left = 1 , right = sa.size() - 1 , med = left; int leftlen = 0 , rightlen = 0 , tlen = t.size(); pair ret; while(left + 1 < right){ med = (left + right) / 2; int corres_len = max( min(leftlen , sparse.query(left , med)) , min(rightlen, sparse.query(med , right)) ); if(corres_len < max(leftlen , rightlen)){ if(leftlen < rightlen) left = med , leftlen = corres_len; else right= med ,rightlen = corres_len; continue; } ret = comp(t , corres_len , sa[med]); //trc(left,med,right,ret); if(ret.second == tlen) return find_range(left,med,right,tlen); if(ret.first == 0) right = med , rightlen = ret.second; else left = med , leftlen = ret.second; } if(sa.size() <= 3){ if(comp(t,0,sa[left]).second==tlen) return find_range(left,left,right,tlen); if(comp(t,0,sa[right]).second==tlen) return find_range(left,right,right,tlen); return make_pair(-1,-1); } med = left + right - med; ret = comp(t , min(leftlen,rightlen) , sa[med]); //trc(left,med,right,ret); if(ret.second == tlen) return find_range(left,med,right,tlen); return make_pair(-1,-1); } }; // Suffix Arrayの使い方(メモリを食うので必要なものだけ使う) // 参照があるのでstringを削除などしないこと /* SuffixArray sa(S); LCPArray lcp(sa); StringSearch search(lcp); */ // 使い方 // 文字列のハッシュ列 Roriha s_rori(S); // 配列のハッシュ列 RollingHash> vrori(v); template struct RollingHash{ using ull = unsigned long long; using Pu = pair; string_t& data; vector hashed , power; int size_; static Pu basis; static constexpr ull rmod = (1ull << 61) - 1; static constexpr ull mul(const ull a,const ull b){ ull l1 = (uint32_t)a, h1 = a>>32, l2 = (uint32_t)b, h2 = b>>32; ull l = l1*l2, m = l1*h2 + l2*h1, h = h1*h2; ull ret = (l & rmod) + (l>>61) + (h << 3) + (m >> 29) + (m << 35 >> 3); if(ret > rmod) ret = (ret & rmod) + (ret>>61); if(ret >= rmod) ret -= rmod; return ret; } static constexpr ull mul_plus(const ull a,const ull b,const ull c){ ull l1 = (uint32_t)a, h1 = a>>32, l2 = (uint32_t)b, h2 = b>>32; ull l = l1*l2, m = l1*h2 + l2*h1, h = h1*h2; ull ret = (l & rmod) + (l >> 61) + (h << 3) + (m >> 29) + (m << 35 >> 3) + c; if(ret > rmod) ret = (ret & rmod) + (ret>>61); if(ret >= rmod) ret -= rmod; return ret; } static constexpr ull modpow(ull a,ull b){ a %= rmod; ull r = 1; while(b) { if(b & 1) r = mul(r , a); a = mul(a , a); b >>= 1; } return r; } static constexpr bool isPrimitive(ull x, vector &ds) { for(ll d : ds) if(d != rmod - 1) { if(modpow( x, (rmod - 1) / d ) == 1) return false; } return true; } static constexpr Pu get_basis(){ vector ds = {2,3,5,7,11,13,31,41,61,151,331,1321}; auto rand_time = chrono::duration_cast(chrono::high_resolution_clock::now().time_since_epoch()).count(); mt19937_64 rng(rand_time); ull a = -1 , b = -1; do{ a = rng() % rmod; }while(isPrimitive(a , ds) == false); do{ b = rng() % rmod; }while(a == b || isPrimitive(b , ds) == false); return Pu(a , b); } // Rolling Hashの構築 O( |S| ) RollingHash(string_t &S) : data(S) , size_((int)S.size()){ // hashed[i] 部分列[0 , i)のハッシュを記録 hashed[0] = (0,0) // power[i] basisのi乗を記録 hashed.resize(size_ + 1); power.resize(size_ + 1); power[0] = Pu(1 , 1); hashed[0] = Pu(0 , 0); for(int i = 1 ; i <= size_ ; i++ ){ power[i].fi = mul( power[i - 1].fi , basis.fi); power[i].se = mul( power[i - 1].se , basis.se); hashed[i].fi = mul_plus( hashed[i - 1].fi , basis.fi , S[i - 1]); hashed[i].se = mul_plus( hashed[i - 1].se , basis.se , S[i - 1]); } } // 部分文字列[ l , r )のハッシュを取得 O(1) Pu get(const int l , const int r){ Pu ret; ret.fi = rmod - mul_plus( hashed[l].fi , power[r-l].fi , rmod - hashed[r].fi ); ret.se = rmod - mul_plus( hashed[l].se , power[r-l].se , rmod - hashed[r].se ); return ret; } // 別の文字列のハッシュを取得 O( |T| ) Pu get_hash(string_t &T){ Pu ret = Pu(0 , 0); for(int i = 0 ; i < (int)T.size() ; i++){ ret.fi = mul_plus(ret.fi , basis.fi , T[i]); ret.se = mul_plus(ret.se , basis.se , T[i]); } return ret; } // 別の文字列と一致判定 O ( |S| + |T| ) // 存在するときは最初の文字を、存在しないときは-1を返す int find(string_t &T){ auto t_hash = get_hash(T); int t_size = (int)(T.size()); // |S| < |T|の時はfor文の中に入らないことに留意する for(int i = 0 ; i <= size_ - t_size ; i++){ if(t_hash == get( i , i + t_size ) ) return i; } return -1; } // 別の文字列と一致判定 O ( |S| + |T| ) // 一致する文字列のindexをすべて返す vector find_all(string_t &T){ auto t_hash = get_hash(T); int t_size = (int)(T.size()); vector ret; // |S| < |T|の時はfor文の中に入らないことに留意する for(int i = 0 ; i <= size_ - t_size ; i++){ if(t_hash == get( i , i + t_size ) ) ret.push_back(i); } return ret; } // Longest Common Prefix(最長共通接頭辞) O( log |S| ) // Sの[al , ar)とTの[bl , br)の最長共通接頭辞の長さを求める // 引数 (文字列Tのハッシュ列 , 文字列Sの開始地点a , 文字列Tの開始地点b) // 返り値 最長共通接頭辞の長さ int LongestCommonPrefix(RollingHash &t , int al , int bl , int ar = -1 , int br = -1){ if(ar == -1) ar = size_; if(br == -1) br = t.size_; int ok = 0 , ng = min(ar - al , br - bl) + 1; while(ok + 1 < ng){ int med = (ok + ng) / 2; if( get(al , med + al) == t.get(bl , med + bl) ) ok = med; else ng = med; } return ok; } // 文字列の大小比較 O( log |S + T| )  // Sの[al , ar)とTの[bl , br)の最長共通接頭辞の長さを求める // 返り値 1 Sのほうが大きい 0 同じ -1 Tのほうが大きい int strcmp(RollingHash &t , int al , int bl , int ar = -1 , int br = -1){ if(ar == -1) ar = size_; if(br == -1) br = t.size_; int n = LongestCommonPrefix(t , al , bl , ar , br); if(al + n == ar) return (bl + n == br) ? 0 : 1; else if(bl + n == br) return -1; else return ( data[al + n] < t.data[bl + n] ) ? 1 : -1; } // 文字列内の最長一致部分文字列を検索 O ( |S| (log|S|)^2 ) int LongestCommonSubString(){ auto func = [&](int len) -> bool { map < Pu , int > m; for(int i = 0 ; i <= size_ - len ; i++){ if( (m[get(i , i + len)] += 1) != 1) return true; } return false; }; int ok = 0 , ng = size_ ; while(ok + 1 < ng){ int med = (ok + ng) / 2; if(func(med)) ok = med; else ng = med; } return ok; } }; // ロリハのハッシュの初期化 template pair RollingHash::basis = RollingHash::get_basis(); using Roriha = RollingHash; // Prime -> 1 {0, 0, 1, 1, 0, 1, 0, 1, ...} vector Primes(int N) { vector A(N + 1, 1); A[0] = A[1] = 0; for (int i = 2; i * i <= N; i++) if (A[i] == 1) for (int j = i << 1; j <= N; j += i) A[j] = 0; return A; } // Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...} vector PrimeSieve(int N) { vector prime = Primes(N); vector ret; for (int i = 0; i < (int)prime.size(); i++) if (prime[i] == 1) ret.push_back(i); return ret; } // Factors (using for fast factorization) // {0, 0, 1, 1, 2, 1, 2, 1, 2, 3, ...} vector Factors(int N) { vector A(N + 1, 1); A[0] = A[1] = 0; for (int i = 2; i * i <= N; i++) if (A[i] == 1) for (int j = i << 1; j <= N; j += i) A[j] = i; return A; } // totient function φ(N)=(1 ~ N , gcd(i,N) = 1) // {0, 1, 1, 2, 4, 2, 6, 4, ... } vector EulersTotientFunction(int N) { vector ret(N + 1, 0); for (int i = 0; i <= N; i++) ret[i] = i; for (int i = 2; i <= N; i++) { if (ret[i] == i) for (int j = i; j <= N; j += i) ret[j] = ret[j] / i * (i - 1); } return ret; } // Divisor ex) 12 -> {1, 2, 3, 4, 6, 12} vector Divisor(long long N) { vector v; for (long long i = 1; i * i <= N; i++) { if (N % i == 0) { v.push_back(i); if (i * i != N) v.push_back(N / i); } } return v; } // Factorization // ex) 18 -> { (2,1) , (3,2) } vector > PrimeFactors(long long N) { vector > ret; for (long long p = 2; p * p <= N; p++) if (N % p == 0) { ret.emplace_back(p, 0); while (N % p == 0) N /= p, ret.back().second++; } if (N >= 2) ret.emplace_back(N, 1); return ret; } // Factorization with Prime Sieve // ex) 18 -> { (2,1) , (3,2) } vector > PrimeFactors(long long N, const vector &prime) { vector > ret; for (auto &p : prime) { if (p * p > N) break; if (N % p == 0) { ret.emplace_back(p, 0); while (N % p == 0) N /= p, ret.back().second++; } } if (N >= 2) ret.emplace_back(N, 1); return ret; } // modpow for mod < 2 ^ 31 long long modpow(long long a, long long n, long long mod) { a %= mod; long long ret = 1; while (n > 0) { if (n & 1) ret = ret * a % mod; a = a * a % mod; n >>= 1; } return ret % mod; }; // Check if r is Primitive Root bool isPrimitiveRoot(long long r, long long mod) { r %= mod; if (r == 0) return false; auto pf = PrimeFactors(mod - 1); for (auto &x : pf) { if (modpow(r, (mod - 1) / x.first, mod) == 1) return false; } return true; } // Get Primitive Root long long PrimitiveRoot(long long mod) { long long ret = 1; while (isPrimitiveRoot(ret, mod) == false) ret++; return ret; } // Extended Euclidean algorithm // solve : ax + by = gcd(a, b) long long extgcd(long long a, long long b, long long &x, long long &y) { if (b == 0) { x = 1; y = 0; return a; } long long d = extgcd(b, a % b, y, x); y -= a / b * x; return d; } // Check if n is Square Number bool isSquare(ll n) { if(n == 0 || n == 1) return true; ll d = (ll)sqrt(n) - 1; while (d * d < n) ++d; return d * d == n; } // return a number of n's digit // zero ... return value if n = 0 (default -> 1) int isDigit(ll n, int zero = 1) { if (n == 0) return zero; int ret = 0; while (n) { n /= 10; ret++; } return ret; } void solve(){ inl(N,M,Q); ins(S); vl K(Q); in(K); // 別に処理 if(M == 1){ SuffixArray sa(S); vi ans(Q); rep(i,Q){ ans[i] = sa.sa[K[i]] + 1; } out(ans); exit(0); } // 周期性を排除 { Roriha rori(S); auto ds = Divisor(N); sort(all(ds)); each(d,ds){ int ok = 1; auto ide = rori.get(0,d); for(int i = 0 ; i < N ; i += d){ if(rori.get(i,i+d) != ide){ ok = 0; break; } } if(ok){ S = S.substr(0,d); M *= (N / d); N = d; break; } } } S += S; SuffixArray sa(S); // 前から見ていく vl ans(Q); ll ki = 0; ll cur = 1; each(x , sa.sa){ if(ki == Q) break; if(x == sz(S)) continue; // 次のものがcur番目 // nxtは? ll nxt; // 短い方 if(x >= N) nxt = cur + 1; // 長い方 else nxt = cur + M - 1; while(ki != Q && K[ki] < nxt){ if(x >= N) ans[ki] = N * M - 2 * N + x + 1; // cur が N*M - 2 * N + x + 1 // 1増えるごとにN後退していく else ans[ki] = N*M - 2*N + x + 1 - (K[ki]-cur)*N; ki++; } cur = nxt; } out(ans); }