#include <algorithm> #include <cstdio> #include <vector> using namespace std; typedef unsigned long long ll; const int DIGITS = 10; const int N_MAX = 25; const int P2_MAX = 200; const ll MASK_LOWER = (~0ULL) >> 32; const ll MASK_UPPER = MASK_LOWER << 32; ll cycle[] = {0, 60, 300, 1500, 15000, 150000, 1500000, 15000000, 150000000, 1500000000, 15000000000, 150000000000, 1500000000000, 15000000000000, 150000000000000, 1500000000000000, 15000000000000000, 150000000000000000, 1500000000000000000, 15000000000000000000ULL}; ll power10[] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000ULL}; ll power2mod[P2_MAX]; struct mat { ll a, b, c; mat(ll a, ll b, ll c) : a(a), b(b), c(c) {} }; vector<ll> start[DIGITS]; char c[N_MAX]; int n; ll d, mod; void add_all(ll& res, ll x, int shift) { // printf("add_all %llu %llu %d\n", res, x, shift); for (int i = 0; i < 64; i++) { if (x & (1ULL << i)) { res = (res + power2mod[i+shift]) % mod; } } } ll mul_mod(ll x, ll y) { ll x_lower = x & MASK_LOWER, x_upper = (x & MASK_UPPER) >> 32; ll y_lower = y & MASK_LOWER, y_upper = (y & MASK_UPPER) >> 32; ll res = 0; add_all(res, x_lower * y_lower, 0); add_all(res, x_upper * y_lower, 32); add_all(res, x_lower * y_upper, 32); add_all(res, x_upper * y_upper, 64); // printf("mul_mod %llu %llu\n", x, y); // printf(" mod=%llu\n", mod); // printf("%llu %llu %llu %llu\n", x_lower, x_upper, y_lower, y_upper); return res; } mat mul_mat(const mat& A, const mat& B) { // printf("%llu %llu %llu\n", A.a, mod, B.a); // ll x = (A.a * B.a + A.b * B.b) % mod; ll x = (mul_mod(A.a, B.a) + mul_mod(A.b, B.b)) % mod; // ll y = (A.a * B.b + A.b * B.c) % mod; ll y = (mul_mod(A.a, B.b) + mul_mod(A.b, B.c)) % mod; // ll z = (A.b * B.b + A.c * A.c) % mod; ll z = (mul_mod(A.b, B.b) + mul_mod(A.c, B.c)) % mod; // printf("%llu %llu %llu\n", x, y, z); return mat(x, y, z); } mat pow_mat(const mat& A, ll n) { if (n == 1) return A; if (n % 2 == 0) return pow_mat(mul_mat(A, A), n/2); return mul_mat(A, pow_mat(mul_mat(A, A), n/2)); } ll fib(ll n) { if (n < 2) return n; return pow_mat(mat(1, 1, 0), n-1).a; } void build_d_n() { while (c[n] != '\0') { d = d * 10 + (c[n] - '0'); n++; } n--; } int main() { c[0] = '1'; scanf("%s", c+1); build_d_n(); // printf("d=%llu, n=%d\n", d, n); mod = power10[n]; //printf("mod=%llu\n", mod); power2mod[0] = 1; for (int i = 1; i < P2_MAX; i++) { power2mod[i] = (2 * power2mod[i-1]) % mod; } for (ll i = 0; i < 60; i++) { ll f = fib(i); // printf("fib(%llu) ", i); // printf("%llu\n", f); start[f % 10].push_back(i); } vector<ll> check = start[d % 10]; vector<ll> tmp; for (int l = 2; l <= n; l++) { // printf("l=%d ", l); tmp.clear(); ll t = cycle[l] / cycle[l-1]; for (ll i = 0; i < t; i++) { for (auto x : check) { ll k = cycle[l-1] * i + x; // printf("%llu ", k); if (fib(k) % power10[l] == d % power10[l]) { tmp.push_back(k); } } } swap(check, tmp); // printf("\n"); } if (check.empty()) { printf("NIE\n"); } else { printf("%llu\n", check[0]); // printf("%s %llu\n", c, fib(check[0]) % mod); } // printf("fib(%llu) = %llu\n", 133971779699176461ULL, fib(133971779699176461ULL)); // printf("fib(%llu) = %llu\n", 16ULL, fib(16ULL)); // printf("fib(%llu) = %llu\n", 30ULL, fib(30ULL)); 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 | #include <algorithm> #include <cstdio> #include <vector> using namespace std; typedef unsigned long long ll; const int DIGITS = 10; const int N_MAX = 25; const int P2_MAX = 200; const ll MASK_LOWER = (~0ULL) >> 32; const ll MASK_UPPER = MASK_LOWER << 32; ll cycle[] = {0, 60, 300, 1500, 15000, 150000, 1500000, 15000000, 150000000, 1500000000, 15000000000, 150000000000, 1500000000000, 15000000000000, 150000000000000, 1500000000000000, 15000000000000000, 150000000000000000, 1500000000000000000, 15000000000000000000ULL}; ll power10[] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000ULL}; ll power2mod[P2_MAX]; struct mat { ll a, b, c; mat(ll a, ll b, ll c) : a(a), b(b), c(c) {} }; vector<ll> start[DIGITS]; char c[N_MAX]; int n; ll d, mod; void add_all(ll& res, ll x, int shift) { // printf("add_all %llu %llu %d\n", res, x, shift); for (int i = 0; i < 64; i++) { if (x & (1ULL << i)) { res = (res + power2mod[i+shift]) % mod; } } } ll mul_mod(ll x, ll y) { ll x_lower = x & MASK_LOWER, x_upper = (x & MASK_UPPER) >> 32; ll y_lower = y & MASK_LOWER, y_upper = (y & MASK_UPPER) >> 32; ll res = 0; add_all(res, x_lower * y_lower, 0); add_all(res, x_upper * y_lower, 32); add_all(res, x_lower * y_upper, 32); add_all(res, x_upper * y_upper, 64); // printf("mul_mod %llu %llu\n", x, y); // printf(" mod=%llu\n", mod); // printf("%llu %llu %llu %llu\n", x_lower, x_upper, y_lower, y_upper); return res; } mat mul_mat(const mat& A, const mat& B) { // printf("%llu %llu %llu\n", A.a, mod, B.a); // ll x = (A.a * B.a + A.b * B.b) % mod; ll x = (mul_mod(A.a, B.a) + mul_mod(A.b, B.b)) % mod; // ll y = (A.a * B.b + A.b * B.c) % mod; ll y = (mul_mod(A.a, B.b) + mul_mod(A.b, B.c)) % mod; // ll z = (A.b * B.b + A.c * A.c) % mod; ll z = (mul_mod(A.b, B.b) + mul_mod(A.c, B.c)) % mod; // printf("%llu %llu %llu\n", x, y, z); return mat(x, y, z); } mat pow_mat(const mat& A, ll n) { if (n == 1) return A; if (n % 2 == 0) return pow_mat(mul_mat(A, A), n/2); return mul_mat(A, pow_mat(mul_mat(A, A), n/2)); } ll fib(ll n) { if (n < 2) return n; return pow_mat(mat(1, 1, 0), n-1).a; } void build_d_n() { while (c[n] != '\0') { d = d * 10 + (c[n] - '0'); n++; } n--; } int main() { c[0] = '1'; scanf("%s", c+1); build_d_n(); // printf("d=%llu, n=%d\n", d, n); mod = power10[n]; //printf("mod=%llu\n", mod); power2mod[0] = 1; for (int i = 1; i < P2_MAX; i++) { power2mod[i] = (2 * power2mod[i-1]) % mod; } for (ll i = 0; i < 60; i++) { ll f = fib(i); // printf("fib(%llu) ", i); // printf("%llu\n", f); start[f % 10].push_back(i); } vector<ll> check = start[d % 10]; vector<ll> tmp; for (int l = 2; l <= n; l++) { // printf("l=%d ", l); tmp.clear(); ll t = cycle[l] / cycle[l-1]; for (ll i = 0; i < t; i++) { for (auto x : check) { ll k = cycle[l-1] * i + x; // printf("%llu ", k); if (fib(k) % power10[l] == d % power10[l]) { tmp.push_back(k); } } } swap(check, tmp); // printf("\n"); } if (check.empty()) { printf("NIE\n"); } else { printf("%llu\n", check[0]); // printf("%s %llu\n", c, fib(check[0]) % mod); } // printf("fib(%llu) = %llu\n", 133971779699176461ULL, fib(133971779699176461ULL)); // printf("fib(%llu) = %llu\n", 16ULL, fib(16ULL)); // printf("fib(%llu) = %llu\n", 30ULL, fib(30ULL)); return 0; } |