#include <iostream> #include <string> #include <vector> #include <cmath> using namespace std; vector<long long> C; long long val; long long mul(long long a, long long b, long long m) { long long r = 0; unsigned long long x = 1; while (x) { if (a&x) { r = (r + b) % m; } b = (b << 1) % m; x <<= 1; } return r; } vector< vector< long long > > matrix_mult(vector< vector< long long > > A, vector< vector< long long > > B, long long m) { vector< vector< long long > > R; R.push_back(vector<long long>()); R.push_back(vector<long long>()); R[0].push_back((mul(A[0][0], B[0][0], m) + mul(A[0][1], B[1][0], m)) % m); R[0].push_back((mul(A[0][0], B[0][1], m) + mul(A[0][1], B[1][1], m)) % m); R[1].push_back((mul(A[1][0], B[0][0], m) + mul(A[1][1], B[1][0], m)) % m); R[1].push_back((mul(A[1][0], B[0][1], m) + mul(A[1][1], B[1][1], m)) % m); return R; } vector< vector< long long > > matrix_pow(vector< vector< long long > > M, long long k, long long m) { if (k == 1) { return M; } return k % 2 ? matrix_mult(matrix_pow(matrix_mult(M, M, m), k / 2, m), M, m) : matrix_pow(matrix_mult(M, M, m), k / 2, m); } long long fib(long long k, long long m) { vector< vector< long long > > J; J.push_back(vector<long long>()); J.push_back(vector<long long>()); J[0].push_back(1); J[0].push_back(1); J[1].push_back(1); J[1].push_back(0); vector< vector< long long > > M = matrix_pow(J, k, m); return M[1][0]; } long long handle_candidate(long long c, long long m) { long long period = 3 * m / 20; long long a = fib(c, m); long long b = fib(c + period, m); int log = 0; long long cm = m; while (cm) { log++; cm /= 10; } // cout << log << " " << "HANDLE CANDIDATE " << c << " " << m << endl; // cout << log << " " << a << " " << b << endl; // cout << log << " " << val << " " << val % m << endl; // getchar(); long long diff = b - a; if (b < a) { diff += m; } long long cand = a; for (int i = 0; i < 10; i++) { //cout << i * period + c << " " << cand << endl; if (cand == val % m) { // cout << log << " " << i * period + c << " " << cand << " IS GOOD" << endl; if (m > val) { return c + i * period; } long long res = handle_candidate(c + i * period, m * 10); if (res != -1) { return res; } } cand = (cand + diff) % m; } return -1; } int main() { ios_base::sync_with_stdio(0); string input; bool special = false; cin >> input; if (input[0] == '0') { if (input.size() == 18) { input[0] = '1'; special = true; } else if (input.size() >= 5) { input = '1' + input; } } val = atoll(input.c_str()); long long mod = pow(10, input.size()); long long mod10 = mod * 10; if (input.size() < 6) { int a = 0, b = 1; int a10 = 0, b10 = 1; for (int i = 2; i < 150010; i++) { int tmp = b; b = (b + a) % mod; a = tmp; tmp = b10; b10 = (b10 + a10) % mod10; a10 = tmp; if (input[0] != '0' && b == val || input[0] == '0' && b == val && b10 != val) { cout << i << endl; break; } if (i == 150009) { cout << "NIE" << endl; } } } if (input.size() > 5) { string last_5 = input.substr(input.size() - 5, 5); int a = 0, b = 1, v = atoi(last_5.c_str()); //cout << v << endl; for (int i = 2; i < 150010; i++) { int tmp = b; b = (b + a) % 100000; a = tmp; if (b == v) { //cout << i << endl; C.push_back(i); } } if (C.empty()) { cout << "NIE" << endl; } else { for (int i = 0; i < C.size(); i++) { long long result = handle_candidate(C[i], 1000000); if (result != -1) { if (special) { cout << result / 10 * 100 + result % 10 << endl; } else { cout << result << endl; } // cout << fib(result, 1000000000000000000ll) << endl; break; } if (i == C.size() - 1) { cout << "NIE" << endl; } } } } return 0; }
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 | #include <iostream> #include <string> #include <vector> #include <cmath> using namespace std; vector<long long> C; long long val; long long mul(long long a, long long b, long long m) { long long r = 0; unsigned long long x = 1; while (x) { if (a&x) { r = (r + b) % m; } b = (b << 1) % m; x <<= 1; } return r; } vector< vector< long long > > matrix_mult(vector< vector< long long > > A, vector< vector< long long > > B, long long m) { vector< vector< long long > > R; R.push_back(vector<long long>()); R.push_back(vector<long long>()); R[0].push_back((mul(A[0][0], B[0][0], m) + mul(A[0][1], B[1][0], m)) % m); R[0].push_back((mul(A[0][0], B[0][1], m) + mul(A[0][1], B[1][1], m)) % m); R[1].push_back((mul(A[1][0], B[0][0], m) + mul(A[1][1], B[1][0], m)) % m); R[1].push_back((mul(A[1][0], B[0][1], m) + mul(A[1][1], B[1][1], m)) % m); return R; } vector< vector< long long > > matrix_pow(vector< vector< long long > > M, long long k, long long m) { if (k == 1) { return M; } return k % 2 ? matrix_mult(matrix_pow(matrix_mult(M, M, m), k / 2, m), M, m) : matrix_pow(matrix_mult(M, M, m), k / 2, m); } long long fib(long long k, long long m) { vector< vector< long long > > J; J.push_back(vector<long long>()); J.push_back(vector<long long>()); J[0].push_back(1); J[0].push_back(1); J[1].push_back(1); J[1].push_back(0); vector< vector< long long > > M = matrix_pow(J, k, m); return M[1][0]; } long long handle_candidate(long long c, long long m) { long long period = 3 * m / 20; long long a = fib(c, m); long long b = fib(c + period, m); int log = 0; long long cm = m; while (cm) { log++; cm /= 10; } // cout << log << " " << "HANDLE CANDIDATE " << c << " " << m << endl; // cout << log << " " << a << " " << b << endl; // cout << log << " " << val << " " << val % m << endl; // getchar(); long long diff = b - a; if (b < a) { diff += m; } long long cand = a; for (int i = 0; i < 10; i++) { //cout << i * period + c << " " << cand << endl; if (cand == val % m) { // cout << log << " " << i * period + c << " " << cand << " IS GOOD" << endl; if (m > val) { return c + i * period; } long long res = handle_candidate(c + i * period, m * 10); if (res != -1) { return res; } } cand = (cand + diff) % m; } return -1; } int main() { ios_base::sync_with_stdio(0); string input; bool special = false; cin >> input; if (input[0] == '0') { if (input.size() == 18) { input[0] = '1'; special = true; } else if (input.size() >= 5) { input = '1' + input; } } val = atoll(input.c_str()); long long mod = pow(10, input.size()); long long mod10 = mod * 10; if (input.size() < 6) { int a = 0, b = 1; int a10 = 0, b10 = 1; for (int i = 2; i < 150010; i++) { int tmp = b; b = (b + a) % mod; a = tmp; tmp = b10; b10 = (b10 + a10) % mod10; a10 = tmp; if (input[0] != '0' && b == val || input[0] == '0' && b == val && b10 != val) { cout << i << endl; break; } if (i == 150009) { cout << "NIE" << endl; } } } if (input.size() > 5) { string last_5 = input.substr(input.size() - 5, 5); int a = 0, b = 1, v = atoi(last_5.c_str()); //cout << v << endl; for (int i = 2; i < 150010; i++) { int tmp = b; b = (b + a) % 100000; a = tmp; if (b == v) { //cout << i << endl; C.push_back(i); } } if (C.empty()) { cout << "NIE" << endl; } else { for (int i = 0; i < C.size(); i++) { long long result = handle_candidate(C[i], 1000000); if (result != -1) { if (special) { cout << result / 10 * 100 + result % 10 << endl; } else { cout << result << endl; } // cout << fib(result, 1000000000000000000ll) << endl; break; } if (i == C.size() - 1) { cout << "NIE" << endl; } } } } return 0; } |