#include <cstdio> #include <iostream> #include <sstream> #include <algorithm> #include <string> #include <vector> using namespace std; const unsigned long long mln=1000000, stotys=100000, stopie=150000;//milion, 100tys, 150tys const unsigned long long okres = mln*mln*mln + (mln*mln*mln)/2; long long F[2*stopie]; long long c; int n; struct triple { long long g, p, q; triple(long long x, long long y, long long z) : g(x), p(y), q(z) {} }; triple ee(long long a, long long b); unsigned long long prod_modulo(unsigned long long a, unsigned long long b); int main() { ios_base::sync_with_stdio(false); string s; cin >> s; n = s.size(); stringstream stin(s); stin >> c; // cout << n << " " << c << endl; int m=n; long long mod=1; while( m>0 ) { mod *= 10; m--; } F[0]=0; F[1]=1; for( int i=2 ; i<300000 ; i++ ) { F[i] = F[i-1] + F[i-2]; F[i] %= mod; } if( n<=5 ) { for( int i=0 ; i<150000 ; i++ ) if( F[i]%mod == c ) { cout << okres + i << endl; return 0; } cout << "NIE" << endl; return 0; } long long pref = c/stotys; long long suf = c%stotys; for( int i=0 ; i<150000 ; i++ ) if( F[i]%stotys == suf ) { long long r1 = F[i]/stotys; long long r2 = F[i+stopie]/stotys; long long interval = r2 + mod/stotys - r1; interval %= (mod/stotys); long long expected = pref + mod/stotys - r1; expected %= (mod/stotys); if( interval==0 ) { if( expected==0 ) { cout << okres + i << endl; return 0; } continue; } triple gcd = ee( mod/stotys, interval); long long per = gcd.g; long long step = gcd.q; while( step<0 ) step += mod/stotys; if( expected % per != 0 ) continue; long long val = prod_modulo( expected/per, step ); val = prod_modulo( val, 150000 ); cout << okres + val + i << endl; return 0; } //W przeciwnym wypadku, gdy nie ma takiej Fk wypisz NIE cout << "NIE" << endl; return 0; } triple ee(long long a, long long b) { if( b==0 ) return triple(a,1,0); triple gcd = ee( b, a%b ); return triple( gcd.g, gcd.q, gcd.p - gcd.q*(a/b) ); } unsigned long long prod_modulo(unsigned long long a, unsigned long long b) { unsigned long long v = 0; a %= okres; b %= okres; unsigned long long A = a; while( b>0 ) { if( b%2==1 ) { v += A; v %= okres; } b /= 2; A *= 2; A %= okres; } }
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 | #include <cstdio> #include <iostream> #include <sstream> #include <algorithm> #include <string> #include <vector> using namespace std; const unsigned long long mln=1000000, stotys=100000, stopie=150000;//milion, 100tys, 150tys const unsigned long long okres = mln*mln*mln + (mln*mln*mln)/2; long long F[2*stopie]; long long c; int n; struct triple { long long g, p, q; triple(long long x, long long y, long long z) : g(x), p(y), q(z) {} }; triple ee(long long a, long long b); unsigned long long prod_modulo(unsigned long long a, unsigned long long b); int main() { ios_base::sync_with_stdio(false); string s; cin >> s; n = s.size(); stringstream stin(s); stin >> c; // cout << n << " " << c << endl; int m=n; long long mod=1; while( m>0 ) { mod *= 10; m--; } F[0]=0; F[1]=1; for( int i=2 ; i<300000 ; i++ ) { F[i] = F[i-1] + F[i-2]; F[i] %= mod; } if( n<=5 ) { for( int i=0 ; i<150000 ; i++ ) if( F[i]%mod == c ) { cout << okres + i << endl; return 0; } cout << "NIE" << endl; return 0; } long long pref = c/stotys; long long suf = c%stotys; for( int i=0 ; i<150000 ; i++ ) if( F[i]%stotys == suf ) { long long r1 = F[i]/stotys; long long r2 = F[i+stopie]/stotys; long long interval = r2 + mod/stotys - r1; interval %= (mod/stotys); long long expected = pref + mod/stotys - r1; expected %= (mod/stotys); if( interval==0 ) { if( expected==0 ) { cout << okres + i << endl; return 0; } continue; } triple gcd = ee( mod/stotys, interval); long long per = gcd.g; long long step = gcd.q; while( step<0 ) step += mod/stotys; if( expected % per != 0 ) continue; long long val = prod_modulo( expected/per, step ); val = prod_modulo( val, 150000 ); cout << okres + val + i << endl; return 0; } //W przeciwnym wypadku, gdy nie ma takiej Fk wypisz NIE cout << "NIE" << endl; return 0; } triple ee(long long a, long long b) { if( b==0 ) return triple(a,1,0); triple gcd = ee( b, a%b ); return triple( gcd.g, gcd.q, gcd.p - gcd.q*(a/b) ); } unsigned long long prod_modulo(unsigned long long a, unsigned long long b) { unsigned long long v = 0; a %= okres; b %= okres; unsigned long long A = a; while( b>0 ) { if( b%2==1 ) { v += A; v %= okres; } b /= 2; A *= 2; A %= okres; } } |