#include <array> #include <cmath> #include <cinttypes> #include <cstdint> #include <iostream> #include <cassert> #ifdef TESTS constexpr const bool tests = true; #else constexpr const bool tests = false; #endif // Matrices template<class T, unsigned n, unsigned m> using mat = std::array<std::array<T, m>, n>; template<class T> using mat2x2 = mat<T, 2, 2>; template<class T> struct defs { static constexpr const mat2x2<T> zero{{ {{0, 0}}, {{0, 0}} }}; static constexpr const mat2x2<T> id {{ {{1, 0}}, {{0, 1}} }}; static constexpr const mat2x2<T> fib {{ {{1, 1}}, {{1, 0}} }}; }; template<class T> constexpr const mat2x2<T> defs<T>::zero; template<class T> constexpr const mat2x2<T> defs<T>::id; template<class T> constexpr const mat2x2<T> defs<T>::fib; // Helper multiplication functions template<class T> struct doubled { static constexpr const int type = 0; }; template<> struct doubled<int8_t> { using type = int16_t; }; template<> struct doubled<uint8_t> { using type = uint16_t; }; template<> struct doubled<int16_t> { using type = int32_t; }; template<> struct doubled<uint16_t> { using type = uint32_t; }; template<> struct doubled<int32_t> { using type = int64_t; }; template<> struct doubled<uint32_t> { using type = uint64_t; }; #ifdef __SIZEOF_INT128__ template<> struct doubled<int64_t> { using type = __int128_t; }; template<> struct doubled<uint64_t> { using type = __uint128_t; }; #endif template<class T, class U = typename doubled<T>::type> __attribute__((const)) constexpr T multiply(T lhs, T rhs, T mod) { return static_cast<T>((static_cast<U>(lhs) * rhs) % mod); } template<class T, int U = doubled<T>::type> __attribute__((const)) T multiply(T lhs, T rhs, T mod) { lhs %= mod; rhs %= mod; T result = 0; while(lhs) { if(lhs % 2 == 1) { result = (result + rhs); if(result >= mod) result -= mod; } lhs /= 2; rhs *= 2; if(rhs >= mod) rhs -= mod; } return result; } template<class T> __attribute__((pure)) mat2x2<T> multiply(const mat2x2<T> &lhs, const mat2x2<T> &rhs, const T mod) { auto result = defs<T>::zero; for(int i = 0; i < 2; ++i) for(int k = 0; k < 2; ++k) for(int j = 0; j < 2; ++j) result[i][j] += multiply(lhs[i][k], rhs[k][j], mod); for(int i = 0; i < 2; ++i) for(int j = 0; j < 2; ++j) result[i][j] %= mod; return result; } template<class T, class Idx=uint64_t> __attribute__((pure)) T fib(Idx idx, const T mod) { auto res = defs<T>::id; auto base = defs<T>::fib; if(idx == 0) return 0; --idx; while(idx) { if(idx % 2 == 1) res = multiply(res, base, mod); base = multiply(base, base, mod); idx /= 2; } return (res[1][0] + res[1][1]) % mod; } template<class T, class Idx=uint64_t> void lift(const Idx idx, const T pattern, const T target, const T power, const Idx lower_period) { if(power > target) { T ans = idx + 6 * target; assert(fib(ans, target) == pattern); throw ans; // quasi-CPS :) } for(Idx i = 0; i < 10; ++i) { auto candidx = idx + i * lower_period; auto cand = fib(candidx, power); if(cand % power == pattern % power) lift(candidx, pattern, target, power * 10, lower_period * 10); } } template<class T> void solve(const T pattern, const T target) { try { for(int i = 0; i < 60; ++i) { auto cand = fib(i, 10u); if(cand % 10 == pattern % 10) lift<T, uint64_t>(i, pattern, target, 100, 60); } } catch(T result) { if(tests) std::cout << "TAK" << std::endl; else std::cout << result << std::endl; return; } std::cout << "NIE" << std::endl; } int main() { std::ios_base::sync_with_stdio(false); std::string str; while(std::cin >> str) { int64_t power = 1; for(size_t i = 0; i < str.size(); ++i) power *= 10; auto pattern = std::stoll(str); solve<uint64_t>(pattern, power); } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 | #include <array> #include <cmath> #include <cinttypes> #include <cstdint> #include <iostream> #include <cassert> #ifdef TESTS constexpr const bool tests = true; #else constexpr const bool tests = false; #endif // Matrices template<class T, unsigned n, unsigned m> using mat = std::array<std::array<T, m>, n>; template<class T> using mat2x2 = mat<T, 2, 2>; template<class T> struct defs { static constexpr const mat2x2<T> zero{{ {{0, 0}}, {{0, 0}} }}; static constexpr const mat2x2<T> id {{ {{1, 0}}, {{0, 1}} }}; static constexpr const mat2x2<T> fib {{ {{1, 1}}, {{1, 0}} }}; }; template<class T> constexpr const mat2x2<T> defs<T>::zero; template<class T> constexpr const mat2x2<T> defs<T>::id; template<class T> constexpr const mat2x2<T> defs<T>::fib; // Helper multiplication functions template<class T> struct doubled { static constexpr const int type = 0; }; template<> struct doubled<int8_t> { using type = int16_t; }; template<> struct doubled<uint8_t> { using type = uint16_t; }; template<> struct doubled<int16_t> { using type = int32_t; }; template<> struct doubled<uint16_t> { using type = uint32_t; }; template<> struct doubled<int32_t> { using type = int64_t; }; template<> struct doubled<uint32_t> { using type = uint64_t; }; #ifdef __SIZEOF_INT128__ template<> struct doubled<int64_t> { using type = __int128_t; }; template<> struct doubled<uint64_t> { using type = __uint128_t; }; #endif template<class T, class U = typename doubled<T>::type> __attribute__((const)) constexpr T multiply(T lhs, T rhs, T mod) { return static_cast<T>((static_cast<U>(lhs) * rhs) % mod); } template<class T, int U = doubled<T>::type> __attribute__((const)) T multiply(T lhs, T rhs, T mod) { lhs %= mod; rhs %= mod; T result = 0; while(lhs) { if(lhs % 2 == 1) { result = (result + rhs); if(result >= mod) result -= mod; } lhs /= 2; rhs *= 2; if(rhs >= mod) rhs -= mod; } return result; } template<class T> __attribute__((pure)) mat2x2<T> multiply(const mat2x2<T> &lhs, const mat2x2<T> &rhs, const T mod) { auto result = defs<T>::zero; for(int i = 0; i < 2; ++i) for(int k = 0; k < 2; ++k) for(int j = 0; j < 2; ++j) result[i][j] += multiply(lhs[i][k], rhs[k][j], mod); for(int i = 0; i < 2; ++i) for(int j = 0; j < 2; ++j) result[i][j] %= mod; return result; } template<class T, class Idx=uint64_t> __attribute__((pure)) T fib(Idx idx, const T mod) { auto res = defs<T>::id; auto base = defs<T>::fib; if(idx == 0) return 0; --idx; while(idx) { if(idx % 2 == 1) res = multiply(res, base, mod); base = multiply(base, base, mod); idx /= 2; } return (res[1][0] + res[1][1]) % mod; } template<class T, class Idx=uint64_t> void lift(const Idx idx, const T pattern, const T target, const T power, const Idx lower_period) { if(power > target) { T ans = idx + 6 * target; assert(fib(ans, target) == pattern); throw ans; // quasi-CPS :) } for(Idx i = 0; i < 10; ++i) { auto candidx = idx + i * lower_period; auto cand = fib(candidx, power); if(cand % power == pattern % power) lift(candidx, pattern, target, power * 10, lower_period * 10); } } template<class T> void solve(const T pattern, const T target) { try { for(int i = 0; i < 60; ++i) { auto cand = fib(i, 10u); if(cand % 10 == pattern % 10) lift<T, uint64_t>(i, pattern, target, 100, 60); } } catch(T result) { if(tests) std::cout << "TAK" << std::endl; else std::cout << result << std::endl; return; } std::cout << "NIE" << std::endl; } int main() { std::ios_base::sync_with_stdio(false); std::string str; while(std::cin >> str) { int64_t power = 1; for(size_t i = 0; i < str.size(); ++i) power *= 10; auto pattern = std::stoll(str); solve<uint64_t>(pattern, power); } } |