#include <iostream> #include <vector> #include <string> #define FOR(i,b,e) for(int i=(b); i <= (e); ++i) #define FORD(i,b,e) for(int i=(b); i >= (e); --i) #define SIZE(c) (int) (c).size() #define FORE(i,c) FOR(i,0,SIZE(c)-1) #define FORDE(i,c) FORD(i,SIZE(c)-1,0) #define PB push_back using namespace std; typedef long long int LLI; typedef vector < LLI > VL; typedef vector < VL > VVL; /*************************************************************************/ LLI getPow(int n) { if (!n) return 1; else return 10 * getPow(n-1); } /*************************************************************************/ typedef VVL Matrix; Matrix zero(int n) { return Matrix(n, VL(n, 0)); } Matrix identity(int n) { Matrix ans = zero(n); FOR(i,0,n-1) ans[i][i] = 1; return ans; } const LLI MOD = getPow(18); const LLI SQRT_MOD = getPow(9); /* returns a * b modulo MOD */ LLI smartMul(LLI a, LLI b) { LLI a0 = a/SQRT_MOD, a1 = a%SQRT_MOD; LLI b0 = b/SQRT_MOD, b1 = b%SQRT_MOD; LLI x0 = (a0 * b1 + a1 * b0)%SQRT_MOD; LLI x1 = (a1 * b1)%MOD; return (x0 * SQRT_MOD + x1)%MOD; } /* multipies square matrices modulo MOD */ Matrix prod(const Matrix &a, const Matrix &b) { int n = SIZE(a); Matrix ans = zero(n); FOR(i,0,n-1) FOR(j,0,n-1) FOR(t,0,n-1) ans[i][t] = (ans[i][t] + smartMul(a[i][j], b[j][t]))%MOD; return ans; } /* quick matrix exponentation modulo MOD */ Matrix pow(const Matrix &a, LLI exp) { if (!exp) return identity(SIZE(a)); else { Matrix temp = pow(a, exp / 2); temp = prod(temp, temp); if (exp%2) temp = prod(temp, a); return temp; } } /*************************************************************************/ /* returns n-th fibonacci number modulo MOD */ LLI getFib(LLI n) { if (!n) return 0; else { Matrix M = {{1, 1}, {1, 0}}; return pow(M, n-1)[0][0]; } } /* returns pisano period for 10^n */ LLI getCycleLen(int n) { switch (n) { case 1: return 60; case 2: return 300; default: return 15 * getPow(n-1); } } /*************************************************************************/ LLI solve(int n, LLI v) { VL ans; FOR(i,0,getCycleLen(1)-1) if (getFib(i)%10 == v%10) ans.PB(i); FOR(i,2,n) { LLI mod = getPow(i); LLI lastCycle = getCycleLen(i-1); LLI cycle = getCycleLen(i); VL temp; for (LLI val : ans) for (LLI newVal = val; newVal < cycle; newVal += lastCycle) if (getFib(newVal)%mod == v%mod) temp.PB(newVal); ans = temp; } if (ans.empty()) return -1; else return ans[0]; } /*************************************************************************/ int main() { ios_base::sync_with_stdio(0); string s; cin >> s; int n = SIZE(s); LLI v = stoll(s); LLI ans = solve(n, v); if (ans == -1) cout << "NIE"; else cout << ans + getCycleLen(n); 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 | #include <iostream> #include <vector> #include <string> #define FOR(i,b,e) for(int i=(b); i <= (e); ++i) #define FORD(i,b,e) for(int i=(b); i >= (e); --i) #define SIZE(c) (int) (c).size() #define FORE(i,c) FOR(i,0,SIZE(c)-1) #define FORDE(i,c) FORD(i,SIZE(c)-1,0) #define PB push_back using namespace std; typedef long long int LLI; typedef vector < LLI > VL; typedef vector < VL > VVL; /*************************************************************************/ LLI getPow(int n) { if (!n) return 1; else return 10 * getPow(n-1); } /*************************************************************************/ typedef VVL Matrix; Matrix zero(int n) { return Matrix(n, VL(n, 0)); } Matrix identity(int n) { Matrix ans = zero(n); FOR(i,0,n-1) ans[i][i] = 1; return ans; } const LLI MOD = getPow(18); const LLI SQRT_MOD = getPow(9); /* returns a * b modulo MOD */ LLI smartMul(LLI a, LLI b) { LLI a0 = a/SQRT_MOD, a1 = a%SQRT_MOD; LLI b0 = b/SQRT_MOD, b1 = b%SQRT_MOD; LLI x0 = (a0 * b1 + a1 * b0)%SQRT_MOD; LLI x1 = (a1 * b1)%MOD; return (x0 * SQRT_MOD + x1)%MOD; } /* multipies square matrices modulo MOD */ Matrix prod(const Matrix &a, const Matrix &b) { int n = SIZE(a); Matrix ans = zero(n); FOR(i,0,n-1) FOR(j,0,n-1) FOR(t,0,n-1) ans[i][t] = (ans[i][t] + smartMul(a[i][j], b[j][t]))%MOD; return ans; } /* quick matrix exponentation modulo MOD */ Matrix pow(const Matrix &a, LLI exp) { if (!exp) return identity(SIZE(a)); else { Matrix temp = pow(a, exp / 2); temp = prod(temp, temp); if (exp%2) temp = prod(temp, a); return temp; } } /*************************************************************************/ /* returns n-th fibonacci number modulo MOD */ LLI getFib(LLI n) { if (!n) return 0; else { Matrix M = {{1, 1}, {1, 0}}; return pow(M, n-1)[0][0]; } } /* returns pisano period for 10^n */ LLI getCycleLen(int n) { switch (n) { case 1: return 60; case 2: return 300; default: return 15 * getPow(n-1); } } /*************************************************************************/ LLI solve(int n, LLI v) { VL ans; FOR(i,0,getCycleLen(1)-1) if (getFib(i)%10 == v%10) ans.PB(i); FOR(i,2,n) { LLI mod = getPow(i); LLI lastCycle = getCycleLen(i-1); LLI cycle = getCycleLen(i); VL temp; for (LLI val : ans) for (LLI newVal = val; newVal < cycle; newVal += lastCycle) if (getFib(newVal)%mod == v%mod) temp.PB(newVal); ans = temp; } if (ans.empty()) return -1; else return ans[0]; } /*************************************************************************/ int main() { ios_base::sync_with_stdio(0); string s; cin >> s; int n = SIZE(s); LLI v = stoll(s); LLI ans = solve(n, v); if (ans == -1) cout << "NIE"; else cout << ans + getCycleLen(n); return 0; } /*************************************************************************/ |