#include <bits/stdc++.h> using namespace std; typedef unsigned long long ll; struct M { ll x11, x12, x21, x22; }; const ll LIM = -1; inline ll mulmod( ll a, ll b, ll m ) { a %= m; b %= m; if (a > b) swap(a, b); if (!a) return 0; if (a < (LIM / b)) return ( (a * b ) % m ); ll res = 0; while ( a ) { if ( a & 1ULL ) res = ( res + b ) % m; a >>= 1; b = ( b << 1 ) % m; } return res; } inline M multi( const M& m1, const M& m2, ll mod ) { M r; r.x11 = ( mulmod( m1.x11, m2.x11, mod ) + mulmod( m1.x12, m2.x21, mod ) ) % mod; r.x12 = ( mulmod( m1.x11, m2.x12, mod ) + mulmod( m1.x12, m2.x22, mod ) ) % mod; r.x21 = ( mulmod( m1.x21, m2.x11, mod ) + mulmod( m1.x22, m2.x21, mod ) ) % mod; r.x22 = ( mulmod( m1.x21, m2.x12, mod ) + mulmod( m1.x22, m2.x22, mod ) ) % mod; return r; } inline M modPow( const M& base, ll p, ll mod ) { M r = {1,0,0,1}; M x = base; while( p ) { if ( p & 1 ) r = multi( r, x, mod ); x = multi( x, x, mod ); p >>= 1; } return r; } const ll mod = 1000000000000000000LL; inline ll fibonacci( ll n ) { M m = {1,1,1,0}; M r = modPow( m, n, mod ); return r.x11; } ll solver( char text[20], int len, int textPos, ll modifyMulti, ll multi[18], ll tenMulti[18] ) { if ( textPos < 0 ) return modifyMulti; int digit = len-textPos-1; for ( int j=0; j<60; ++j ) { ll v = modifyMulti + j*multi[ digit ]; ll fib = fibonacci( v ); fib /= tenMulti[ digit ]; if ( fib == 0 ) continue; fib %= 10; if ( (int)(text[textPos]-'0') == (int)fib ) { ll res = solver( text, len, textPos-1, modifyMulti + j*multi[ digit ], multi, tenMulti ); if ( res != -1 ) return res; } } return -1; } int main() { ios::sync_with_stdio( 0 ); char text[20]; ll tenMulti[18] = {1}; ll multi[18] = { 1, 60, 300, 1500 }; for ( int i=4; i<18; ++i ) multi[i] = multi[i-1]*10; for ( int i=1; i< 18; ++i ) tenMulti[i] = tenMulti[i-1]*10; ll noFib[11] = { 4,6,10,12,14,18,20,22,26,28,30 }; ll fibMask = (1ULL << 5) - 1; cin >> text; int len = strlen( text ); ll textNumber = 0; for ( int i=len-1; i>=0; --i ) textNumber += (ll)(text[i]-'0') * tenMulti[ len-1-i ]; if ( len >= 5 ) for ( int i=0; i<11; ++i ) { if ( ( textNumber & fibMask ) == noFib[i] ) { cout << "NIE" << endl; return 0; } } ll res = solver( text, len, len-1, 0, multi, tenMulti ); if ( res == -1 ) cout << "NIE" << endl; else cout << res+1 << 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 | #include <bits/stdc++.h> using namespace std; typedef unsigned long long ll; struct M { ll x11, x12, x21, x22; }; const ll LIM = -1; inline ll mulmod( ll a, ll b, ll m ) { a %= m; b %= m; if (a > b) swap(a, b); if (!a) return 0; if (a < (LIM / b)) return ( (a * b ) % m ); ll res = 0; while ( a ) { if ( a & 1ULL ) res = ( res + b ) % m; a >>= 1; b = ( b << 1 ) % m; } return res; } inline M multi( const M& m1, const M& m2, ll mod ) { M r; r.x11 = ( mulmod( m1.x11, m2.x11, mod ) + mulmod( m1.x12, m2.x21, mod ) ) % mod; r.x12 = ( mulmod( m1.x11, m2.x12, mod ) + mulmod( m1.x12, m2.x22, mod ) ) % mod; r.x21 = ( mulmod( m1.x21, m2.x11, mod ) + mulmod( m1.x22, m2.x21, mod ) ) % mod; r.x22 = ( mulmod( m1.x21, m2.x12, mod ) + mulmod( m1.x22, m2.x22, mod ) ) % mod; return r; } inline M modPow( const M& base, ll p, ll mod ) { M r = {1,0,0,1}; M x = base; while( p ) { if ( p & 1 ) r = multi( r, x, mod ); x = multi( x, x, mod ); p >>= 1; } return r; } const ll mod = 1000000000000000000LL; inline ll fibonacci( ll n ) { M m = {1,1,1,0}; M r = modPow( m, n, mod ); return r.x11; } ll solver( char text[20], int len, int textPos, ll modifyMulti, ll multi[18], ll tenMulti[18] ) { if ( textPos < 0 ) return modifyMulti; int digit = len-textPos-1; for ( int j=0; j<60; ++j ) { ll v = modifyMulti + j*multi[ digit ]; ll fib = fibonacci( v ); fib /= tenMulti[ digit ]; if ( fib == 0 ) continue; fib %= 10; if ( (int)(text[textPos]-'0') == (int)fib ) { ll res = solver( text, len, textPos-1, modifyMulti + j*multi[ digit ], multi, tenMulti ); if ( res != -1 ) return res; } } return -1; } int main() { ios::sync_with_stdio( 0 ); char text[20]; ll tenMulti[18] = {1}; ll multi[18] = { 1, 60, 300, 1500 }; for ( int i=4; i<18; ++i ) multi[i] = multi[i-1]*10; for ( int i=1; i< 18; ++i ) tenMulti[i] = tenMulti[i-1]*10; ll noFib[11] = { 4,6,10,12,14,18,20,22,26,28,30 }; ll fibMask = (1ULL << 5) - 1; cin >> text; int len = strlen( text ); ll textNumber = 0; for ( int i=len-1; i>=0; --i ) textNumber += (ll)(text[i]-'0') * tenMulti[ len-1-i ]; if ( len >= 5 ) for ( int i=0; i<11; ++i ) { if ( ( textNumber & fibMask ) == noFib[i] ) { cout << "NIE" << endl; return 0; } } ll res = solver( text, len, len-1, 0, multi, tenMulti ); if ( res == -1 ) cout << "NIE" << endl; else cout << res+1 << endl; return 0; } |