#include <bits/stdc++.h> using namespace std; typedef long long ll; ll addmod( ll x, ll y, ll m ) { x %= m; y %= m; ll sum = x-m+y; // -m <= sum < m-1 return sum < 0 ? sum + m : sum; } ll timesmod( ll x, ll y, ll m ) { x %= m; y %= m; ll a = x < y ? x : y; // min ll b = x < y ? y : x; // max ll product = 0; for (; a != 0; a >>= 1, b = addmod(b,b,m) ) if (a&1) product = addmod(product,b,m); return product; } struct Mat { // row-major ll t[2][2]; Mat mult(const Mat &lhs, ll m) { Mat ret {{{0, 0}, {0, 0}}}; for(size_t i = 0; i < 2; ++i) for(size_t j = 0; j < 2; ++j) for(size_t k = 0; k < 2; ++k) { ret.t[i][j] += timesmod((t[i][k] % m), (lhs.t[k][j] % m), m); ret.t[i][j] %= m; // modulo first, ask questions later; just to be sure } return ret; } Mat & operator%=(ll m) { for(ll *p : {&t[0][0], &t[0][1], &t[1][0], &t[1][1]}) *p %= m; } /* b00 = a00*a00 + a01*a10 b01 = a00*a01 + a01*a11 b10 = a10*a00 + a11*a10 b11 = a10*a01 + a11*a11 b00 = a00*a00 + a01*a10 b01 = a01*(a00 + a11) b10 = a10*(a00 + a11) b11 = a10*a01 + a11*a11 */ void inplaceSqr(ll m) { *this %= m; const ll q = (t[0][0] + t[1][1]) % m; t[0][0] = timesmod(t[0][0], t[0][0], m) + timesmod(t[0][1], t[1][0], m); t[1][1] = timesmod(t[0][1], t[1][0], m) + timesmod(t[1][1], t[1][1], m); t[0][1] = timesmod(t[0][1], q, m); t[1][0] = timesmod(t[1][0], q, m); *this %= m; // thou shalt modulo all things } }; const Mat I {{{1, 0}, {0, 1}}}; const Mat F {{{1, 1}, {1, 0}}}; Mat ebs(Mat A, ll e, ll m) { if(e == 0) return I; A %= m; if(e == 1) return A; if(e % 2 == 0) { A.inplaceSqr(m); return ebs(move(A), e/2, m); } // assert(e % 2 == 1); Mat B = A; A.inplaceSqr(m); return ebs(move(A), e/2, m).mult(B, m); } ll fib(ll x, ll m) { if(x == 0) return 0; return ebs(F, x-1, m).t[0][0]; } ll getdig(ll x, size_t i) { for(; i; --i) x /= 10; return x % 10; } const ll cycles[] { 60LL, 300LL, 1500LL, 15000LL, 150000LL, 1500000LL, 15000000LL, 150000000LL, 1500000000LL, 15000000000LL, 150000000000LL, 1500000000000LL, 15000000000000LL, 150000000000000LL, 1500000000000000LL, 15000000000000000LL, 150000000000000000LL, 1500000000000000000LL, }; int main() { /* for(ll i = 0; i < 1500; ++i) fprintf(stderr, "%20lld %20lld\n", i, fib(i, 1000LL)); fprintf(stderr, "\n%20lld %20lld\n", 1525LL, fib(1525, 1000000000000000000LL)); */ char cbuf[19]; scanf("%s", cbuf); ll c; sscanf(cbuf, "%lld", &c); if(c == 0) { printf("0\n"); return 0; } string sc = cbuf; vector<ll> targets(60), hits; iota(targets.begin(), targets.end(), 0); for(ll x : targets) if(c % 10 == fib(x, 10)) hits.push_back(x); ll tenpow = 10; for(size_t i = 1; i < sc.size(); ++i) { /* sort(hits.begin(), hits.end()); for(ll x : hits) fprintf(stderr, "%lld\t", x); fprintf(stderr, "\n"); */ tenpow *= 10; targets.clear(); targets.swap(hits); for(size_t j = targets.size() - 1; j < targets.size(); --j) // damn hackers!! for(size_t k = 1; i <= 2 ? k < 5 : k < 10; ++k) targets.push_back(targets[j] + k*cycles[i-1]); /* sort(targets.begin(), targets.end()); for(ll x : targets) fprintf(stderr, "%lld\t", x); fprintf(stderr, "\n\n"); */ for(ll x : targets) { ll f = fib(x, tenpow); if(getdig(c, i) == getdig(f, i)) hits.push_back(x); } } if(hits.empty()) { printf("NIE\n"); return 0; } /* for(ll x : hits) fprintf(stderr, "%lld\t", x); fprintf(stderr, "\n"); */ printf("%lld\n", hits[0] + cycles[sc.size()-1]); 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 | #include <bits/stdc++.h> using namespace std; typedef long long ll; ll addmod( ll x, ll y, ll m ) { x %= m; y %= m; ll sum = x-m+y; // -m <= sum < m-1 return sum < 0 ? sum + m : sum; } ll timesmod( ll x, ll y, ll m ) { x %= m; y %= m; ll a = x < y ? x : y; // min ll b = x < y ? y : x; // max ll product = 0; for (; a != 0; a >>= 1, b = addmod(b,b,m) ) if (a&1) product = addmod(product,b,m); return product; } struct Mat { // row-major ll t[2][2]; Mat mult(const Mat &lhs, ll m) { Mat ret {{{0, 0}, {0, 0}}}; for(size_t i = 0; i < 2; ++i) for(size_t j = 0; j < 2; ++j) for(size_t k = 0; k < 2; ++k) { ret.t[i][j] += timesmod((t[i][k] % m), (lhs.t[k][j] % m), m); ret.t[i][j] %= m; // modulo first, ask questions later; just to be sure } return ret; } Mat & operator%=(ll m) { for(ll *p : {&t[0][0], &t[0][1], &t[1][0], &t[1][1]}) *p %= m; } /* b00 = a00*a00 + a01*a10 b01 = a00*a01 + a01*a11 b10 = a10*a00 + a11*a10 b11 = a10*a01 + a11*a11 b00 = a00*a00 + a01*a10 b01 = a01*(a00 + a11) b10 = a10*(a00 + a11) b11 = a10*a01 + a11*a11 */ void inplaceSqr(ll m) { *this %= m; const ll q = (t[0][0] + t[1][1]) % m; t[0][0] = timesmod(t[0][0], t[0][0], m) + timesmod(t[0][1], t[1][0], m); t[1][1] = timesmod(t[0][1], t[1][0], m) + timesmod(t[1][1], t[1][1], m); t[0][1] = timesmod(t[0][1], q, m); t[1][0] = timesmod(t[1][0], q, m); *this %= m; // thou shalt modulo all things } }; const Mat I {{{1, 0}, {0, 1}}}; const Mat F {{{1, 1}, {1, 0}}}; Mat ebs(Mat A, ll e, ll m) { if(e == 0) return I; A %= m; if(e == 1) return A; if(e % 2 == 0) { A.inplaceSqr(m); return ebs(move(A), e/2, m); } // assert(e % 2 == 1); Mat B = A; A.inplaceSqr(m); return ebs(move(A), e/2, m).mult(B, m); } ll fib(ll x, ll m) { if(x == 0) return 0; return ebs(F, x-1, m).t[0][0]; } ll getdig(ll x, size_t i) { for(; i; --i) x /= 10; return x % 10; } const ll cycles[] { 60LL, 300LL, 1500LL, 15000LL, 150000LL, 1500000LL, 15000000LL, 150000000LL, 1500000000LL, 15000000000LL, 150000000000LL, 1500000000000LL, 15000000000000LL, 150000000000000LL, 1500000000000000LL, 15000000000000000LL, 150000000000000000LL, 1500000000000000000LL, }; int main() { /* for(ll i = 0; i < 1500; ++i) fprintf(stderr, "%20lld %20lld\n", i, fib(i, 1000LL)); fprintf(stderr, "\n%20lld %20lld\n", 1525LL, fib(1525, 1000000000000000000LL)); */ char cbuf[19]; scanf("%s", cbuf); ll c; sscanf(cbuf, "%lld", &c); if(c == 0) { printf("0\n"); return 0; } string sc = cbuf; vector<ll> targets(60), hits; iota(targets.begin(), targets.end(), 0); for(ll x : targets) if(c % 10 == fib(x, 10)) hits.push_back(x); ll tenpow = 10; for(size_t i = 1; i < sc.size(); ++i) { /* sort(hits.begin(), hits.end()); for(ll x : hits) fprintf(stderr, "%lld\t", x); fprintf(stderr, "\n"); */ tenpow *= 10; targets.clear(); targets.swap(hits); for(size_t j = targets.size() - 1; j < targets.size(); --j) // damn hackers!! for(size_t k = 1; i <= 2 ? k < 5 : k < 10; ++k) targets.push_back(targets[j] + k*cycles[i-1]); /* sort(targets.begin(), targets.end()); for(ll x : targets) fprintf(stderr, "%lld\t", x); fprintf(stderr, "\n\n"); */ for(ll x : targets) { ll f = fib(x, tenpow); if(getdig(c, i) == getdig(f, i)) hits.push_back(x); } } if(hits.empty()) { printf("NIE\n"); return 0; } /* for(ll x : hits) fprintf(stderr, "%lld\t", x); fprintf(stderr, "\n"); */ printf("%lld\n", hits[0] + cycles[sc.size()-1]); return 0; } |