/* -*- coding: utf-8 -*- * * 2030.cc: No.2030 Googol Strings - yukicoder */ #include #include #include using namespace std; /* constant */ const int MAX_N = 1000000; const int P = 4073; const int MOD = 1000000009; const int INF = 1 << 30; /* typedef */ template struct MI { int v; MI(): v() {} MI(int _v): v(_v % MOD) {} MI(long long _v): v(_v % MOD) {} MI operator+(const MI m) const { return MI(v + m.v); } MI operator-(const MI m) const { return MI(v + MOD - m.v); } MI operator*(const MI m) const { return MI((long long)v * m.v); } MI &operator+=(const MI m) { return (*this = *this + m); } MI &operator-=(const MI m) { return (*this = *this - m); } MI &operator*=(const MI m) { return (*this = *this * m); } MI pow(int n) const { // a^n % MOD MI pm = 1, a = *this; while (n > 0) { if (n & 1) pm *= a; a *= a; n >>= 1; } return pm; } MI inv() const { return pow(MOD - 2); } MI operator/(const MI m) const { return *this * m.inv(); } MI &operator/=(const MI m) { return (*this = *this / m); } bool operator==(const MI m) const { return v == m.v; } bool operator!=(const MI m) const { return v != m.v; } }; typedef MI mi; /* global variables */ char x[MAX_N + 4], y[MAX_N + 4]; mi pes[MAX_N + 1], invpes[MAX_N + 1]; mi xrhs[MAX_N + 1], yrhs[MAX_N + 1]; /* subroutines */ inline void prep_rhash(int n) { pes[0] = invpes[0] = 1; pes[1] = P; invpes[1] = pes[1].inv(); for (int i = 2; i <= n; i++) { pes[i] = pes[i - 1] * P; invpes[i] = invpes[i - 1] * invpes[1]; } } inline int s2rh(mi rh[], const char s[]) { int k = 0; for (; s[k]; k++) rh[k + 1] = rh[k] + pes[k] * s[k]; return k; } inline mi rhash(mi rhs[], int i, int j) { return (rhs[j] - rhs[i]) * invpes[i]; } bool rpt(int n, mi rhs[], int d, mi h) { for (int i = 0; i + d <= n; i += d) if (rhash(rhs, i, i + d) != h) return false; return true; } /* main */ int main() { prep_rhash(MAX_N); int tn; scanf("%d", &tn); while (tn--) { scanf("%s%s", x, y); int n = s2rh(xrhs, x); int m = s2rh(yrhs, y); if (n != m) { if (n < m) { int minl = INF; for (int p = 1; p * p <= n; p++) if (n % p == 0) { if (rpt(n, xrhs, p, xrhs[p])) minl = min(minl, p); int q = n / p; if (q != p && rpt(n, xrhs, q, xrhs[q])) minl = min(minl, q); } //printf("minl=%d\n", minl); if (minl < INF && m % minl == 0 && rpt(m, yrhs, minl, xrhs[minl])) { puts("Y"); continue; } } else { int minl = INF; for (int p = 1; p * p <= m; p++) if (m % p == 0) { if (rpt(m, yrhs, p, yrhs[p])) minl = min(minl, p); int q = m / p; if (q != p && rpt(m, yrhs, q, yrhs[q])) minl = min(minl, q); } //printf("minl=%d\n", minl); if (minl < INF && n % minl == 0 && rpt(n, xrhs, minl, xrhs[minl])) { puts("X"); continue; } } } int l = max(n, m); for (int i = 0; i < l; i++) { char xi = x[i % n], yi = y[i % m]; if (xi != yi) { if (xi > yi) puts("X"); else puts("Y"); break; } } } return 0; }