#include <bits/stdc++.h> using namespace std; #define REP(i,a,b) for (int i = (a); i <= (b); ++i) #define REPD(i,a,b) for (int i = (a); i >= (b); --i) #define FORI(i,n) REP(i,1,n) #define FOR(i,n) REP(i,0,int(n)-1) #define mp make_pair #define pb push_back #define pii pair<int,int> #define vi vector<int> #define ll long long #define SZ(x) int((x).size()) #define DBG(v) cerr << #v << " = " << (v) << endl; #define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++) #define fi first #define se second long long mult(long long a, long long b, long long p) { if (b==0) return 0; long long res = mult(a,b/2,p); res = res + res; if (res >= p) res -= p; if (b&1) { res = res + a; if (res >= p) res -= p; } return res; } long long qpow(long long a, long long n, long long p) { if (n==0) return 1; long long b = qpow(a,n/2,p); b = mult(b,b,p); if (n&1) b = mult(b,a,p); return b; } // phi(2^a*5^b) long long phi(long long m) { long long p = 1; while (m%2 == 0) { p *= 2; m /= 2; } if (p >= 2) p /= 2; if (m >= 5) m = m/5*4; return p*m; } // start + solve*step = fin mod mod long long solve(long long start, long long step, long long fin, long long mod) { //printf("solve %lld %lld %lld %lld\n", start, step, fin, mod); fin -= start; if (fin < 0) fin += mod; long long g = __gcd(mod, step); if (fin%g != 0) return -1; step /= g; fin /= g; mod /= g; long long res = qpow(step, phi(mod)-1, mod); res = mult(res, fin, mod); return res; } long long per2(long long x) { return x*3/2; } long long per5(long long x) { return x*4; } long long per10(long long x) { long long res = x/2*3; while(res%4!=0) res*=2; return res; } // wejscie char s[33]; int n; long long goal; // bazy long long base2, base5, base10; char magic[33] = "11110101110101011101010111010101"; long long r4[4]; bool add(long long res) { int p = res%4; if (r4[p] != -1) return false; r4[p] = res; FOR(i,4) if (r4[i]==-1) return false; return true; } long long get(int B) { int right = (n+1)/2, left = n-right; long long lbase = 1, rbase = 1; FOR(i,left) lbase *= B; FOR(i,right) rbase *= B; long long base = lbase * rbase; long long pref = (goal % base) / rbase, suff = goal % rbase; if (B==2) base2=per2(base); if (B==5) base5=base; if (B==10) base10=per10(base); long long rper; if (B==2) rper=per2(rbase); if (B==5) rper=per5(rbase); if (B==10) rper=per10(rbase); //printf("B = %d, left = %d, right = %d, lbase = %lld, rbase = %lld, pref = %lld, suff = %lld, rper = %lld\n", B, left, right, lbase, rbase, pref, suff, rper); long long f0 = 0, f1 = 1, f2 = 1; REP(i,2,rper-1) { f2 = f0+f1; if (f2 >= base) f2 -= base; f0 = f1; f1 = f2; } // f2 = fib(rper-1) long long g0 = -1, g1 = 1, g2 = 0; FOR(i,rper) { f2 = f0+f1; if (f2 >= base) f2 -= base; f0=f1; f1=f2; g2 = g0+g1; if (g2 >= base) g2 -= base; g0=g1; g1=g2; if (B==5 && r4[i%4]==-1) continue; //printf("i=%d, f2 = %lld, g2 = %lld\n", i, f2, g2); // f2=fib(rper+i), g2=fib(i) long long last = g2%rbase; if (last != suff) continue; long long start = (g2%base)/rbase; long long step = (f2%base)/rbase - start; if (step < 0) step += lbase; long long row = solve(start, step, pref, lbase); if (row == -1) continue; long long res = row*rper+i; if (B!=2) return res; if (B==2) { bool en = add(res); if (en) return res; } } if (B==2) FOR(i,4) if (r4[i] != -1) return 0; return -1; } long long inv(long long a, long long m) { return qpow(a, phi(m)-1, m); } long long calc(long long a, long long ma, long long b, long long mb) { long long tot = ma*mb; long long pa = mult(mb, inv(mb,ma), tot); long long pb = mult(ma, inv(ma,mb), tot); long long res = mult(a, pa, tot) + mult(b, pb, tot); if (res >= tot) res -= tot; return res; } int main () { scanf("%s", s); goal = 0; for (n=0; s[n]; n++) goal = 10LL*goal + (s[n]-'0'); int tt = goal % 32; if (magic[tt] == '0') { printf("NIE\n"); return 0; } if (n<6) { long long r10 = get(10); if (r10 == -1) return 0; if (r10 < 40) r10 += base10; printf("%lld\n", r10); return 0; } FOR(i,4) r4[i]=-1; long long r2 = get(2); long long r5 = get(5); if (r2 == -1 || r5 == -1) { printf("NIE\n"); return 0; } r2 = r4[r5%4]; long long res = calc(r2, base2, r5%base5, base5); long long per = base2*base5; if (res < 40) res += per; // czy nie ma za malo cyfr printf("%lld\n", res); }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 | #include <bits/stdc++.h> using namespace std; #define REP(i,a,b) for (int i = (a); i <= (b); ++i) #define REPD(i,a,b) for (int i = (a); i >= (b); --i) #define FORI(i,n) REP(i,1,n) #define FOR(i,n) REP(i,0,int(n)-1) #define mp make_pair #define pb push_back #define pii pair<int,int> #define vi vector<int> #define ll long long #define SZ(x) int((x).size()) #define DBG(v) cerr << #v << " = " << (v) << endl; #define FOREACH(i,t) for (typeof(t.begin()) i=t.begin(); i!=t.end(); i++) #define fi first #define se second long long mult(long long a, long long b, long long p) { if (b==0) return 0; long long res = mult(a,b/2,p); res = res + res; if (res >= p) res -= p; if (b&1) { res = res + a; if (res >= p) res -= p; } return res; } long long qpow(long long a, long long n, long long p) { if (n==0) return 1; long long b = qpow(a,n/2,p); b = mult(b,b,p); if (n&1) b = mult(b,a,p); return b; } // phi(2^a*5^b) long long phi(long long m) { long long p = 1; while (m%2 == 0) { p *= 2; m /= 2; } if (p >= 2) p /= 2; if (m >= 5) m = m/5*4; return p*m; } // start + solve*step = fin mod mod long long solve(long long start, long long step, long long fin, long long mod) { //printf("solve %lld %lld %lld %lld\n", start, step, fin, mod); fin -= start; if (fin < 0) fin += mod; long long g = __gcd(mod, step); if (fin%g != 0) return -1; step /= g; fin /= g; mod /= g; long long res = qpow(step, phi(mod)-1, mod); res = mult(res, fin, mod); return res; } long long per2(long long x) { return x*3/2; } long long per5(long long x) { return x*4; } long long per10(long long x) { long long res = x/2*3; while(res%4!=0) res*=2; return res; } // wejscie char s[33]; int n; long long goal; // bazy long long base2, base5, base10; char magic[33] = "11110101110101011101010111010101"; long long r4[4]; bool add(long long res) { int p = res%4; if (r4[p] != -1) return false; r4[p] = res; FOR(i,4) if (r4[i]==-1) return false; return true; } long long get(int B) { int right = (n+1)/2, left = n-right; long long lbase = 1, rbase = 1; FOR(i,left) lbase *= B; FOR(i,right) rbase *= B; long long base = lbase * rbase; long long pref = (goal % base) / rbase, suff = goal % rbase; if (B==2) base2=per2(base); if (B==5) base5=base; if (B==10) base10=per10(base); long long rper; if (B==2) rper=per2(rbase); if (B==5) rper=per5(rbase); if (B==10) rper=per10(rbase); //printf("B = %d, left = %d, right = %d, lbase = %lld, rbase = %lld, pref = %lld, suff = %lld, rper = %lld\n", B, left, right, lbase, rbase, pref, suff, rper); long long f0 = 0, f1 = 1, f2 = 1; REP(i,2,rper-1) { f2 = f0+f1; if (f2 >= base) f2 -= base; f0 = f1; f1 = f2; } // f2 = fib(rper-1) long long g0 = -1, g1 = 1, g2 = 0; FOR(i,rper) { f2 = f0+f1; if (f2 >= base) f2 -= base; f0=f1; f1=f2; g2 = g0+g1; if (g2 >= base) g2 -= base; g0=g1; g1=g2; if (B==5 && r4[i%4]==-1) continue; //printf("i=%d, f2 = %lld, g2 = %lld\n", i, f2, g2); // f2=fib(rper+i), g2=fib(i) long long last = g2%rbase; if (last != suff) continue; long long start = (g2%base)/rbase; long long step = (f2%base)/rbase - start; if (step < 0) step += lbase; long long row = solve(start, step, pref, lbase); if (row == -1) continue; long long res = row*rper+i; if (B!=2) return res; if (B==2) { bool en = add(res); if (en) return res; } } if (B==2) FOR(i,4) if (r4[i] != -1) return 0; return -1; } long long inv(long long a, long long m) { return qpow(a, phi(m)-1, m); } long long calc(long long a, long long ma, long long b, long long mb) { long long tot = ma*mb; long long pa = mult(mb, inv(mb,ma), tot); long long pb = mult(ma, inv(ma,mb), tot); long long res = mult(a, pa, tot) + mult(b, pb, tot); if (res >= tot) res -= tot; return res; } int main () { scanf("%s", s); goal = 0; for (n=0; s[n]; n++) goal = 10LL*goal + (s[n]-'0'); int tt = goal % 32; if (magic[tt] == '0') { printf("NIE\n"); return 0; } if (n<6) { long long r10 = get(10); if (r10 == -1) return 0; if (r10 < 40) r10 += base10; printf("%lld\n", r10); return 0; } FOR(i,4) r4[i]=-1; long long r2 = get(2); long long r5 = get(5); if (r2 == -1 || r5 == -1) { printf("NIE\n"); return 0; } r2 = r4[r5%4]; long long res = calc(r2, base2, r5%base5, base5); long long per = base2*base5; if (res < 40) res += per; // czy nie ma za malo cyfr printf("%lld\n", res); } |