05: Moon Landing program, 05 moon landing Program

05: Moon Landing program, 05 moon landing Program

Total time limit:

40000 ms

 

Time limit for a single test point:

4000 ms

 

Memory limit:

256000kB

Description

HJA is learning mathematics with his students, so he has a very simple mathematical problem: finding the minimum Natural Number x that satisfies ax Limit = B (mod p.

 

 

For 30% of data, 1 ≤ p ≤ 1000.

For 100% of data, 1 ≤ a, B <p ≤ 1e12.

Input

Three integers a, B, and p in the input data row. We ensure that p is a prime number.

Output

An integer in a row represents the smallest natural number x. If such an integer does not exist, the output is-1.

Sample Input

2 1 3

Sample output

0

Source

Zhonghaoxi

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• Question

 

After doing this, we can find the greatness of pb_ds ....

Pb_ds 80 20000 + ms not required

AC 10000 + ms is used ..

 

1 # include <iostream> 2 # include <cstdio> 3 # include <cstring> 4 # include <cmath> 5 # include <map> 6 # define LL long 7 using namespace std; 8 LL a, B, c; 9 map <LL, LL> mp; 10 LL fastmul (LL x, LL p) 11 {12 LL now = x; 13 LL ans = 0; 14 while (p) 15 {16 if (p & 1) 17 {18 -- p; 19 ans = (ans + now) % c; 20} 21 p >>= 1; 22 now = (now + now) % c; 23} 24 return (ans) % c; 25} 26 LL fastpow (LL, LL p, LL c) 27 {28 LL base = a; LL ans = 1; 29 while (p! = 0) 30 {31 if (p % 2 = 1) ans = (fastmul (ans, base) % c; 32 base = (fastmul (base, base )) % c; 33 p = p> 1; 34} 35 return ans; 36} 37 int main () 38 {39 // a ^ x = B (mod c) 40/* LL x, y, mod; 41 cin> x> y> mod; 42 c = mod; 43 a = x; 44 B = y; */45 cin> a> B> c; 46 LL m = ceil (sqrt (c); // You must round up 47 mp. clear (); 48 if (a % c = 0) 49 {50 printf ("-1 \ n"); 51 return 0; 52} 53 // solution condition 54 LL ans of the ferma small theorem; // store the result of each enumeration B * a ^ j55 for (LL j = 0; j <= m; j ++) // a ^ (I * m) = B * a ^ j56 {57 if (j = 0) 58 {59 ans = B % c; 60 mp [ans] = j; // process a ^ 0 = 1 61 continue; 62} 63 ans = (fastmul (ans, a) % c; // a ^ j 64 mp [ans] = j; // store the result of each enumeration 65} 66 LL t = fastpow (a, m, c); 67 ans = 1; // a ^ (I * m) 68 LL flag = 0; 69 for (LL I = 1; I <= m; I ++) 70 {71 ans = (fastmul (ans, t) % c; 72 if (mp [ans]) 73 {74 LL out = fastmul (I, m)-mp [ans]; // x = I * m-j75 printf ("% lld \ n", (out % c + c) % c); 76 flag = 1; 77 break; 78} 79 80} 81 if (! Flag) 82 printf ("-1 \ n"); 83 return 0; 84}80 1 # include <iostream> 2 # include <cstdio> 3 # include <cstring> 4 # include <cmath> 5 # include <map> 6 # include <ext/pb_ds/ assoc_container.hpp> 7 # include <ext/pb_ds/hash_policy.hpp> 8 # define LL long 9 using namespace std; 10 using namespace _ gnu_pbds; 11 LL a, B, c; 12 gp_hash_table <LL, LL> mp; 13 LL fastmul (LL x, LL p) 14 {15 LL now = x; 16 LL ans = 0; 17 while (p) 18 {19 if (p & 1) 20 {21 -- p; 22 ans = (ans + now) % c; 23} 24 p >>=1; 25 now = (now + now) % c; 26} 27 return (ans) % c; 28} 29 LL fastpow (LL, LL p, LL c) 30 {31 LL base = a; LL ans = 1; 32 while (p! = 0) 33 {34 if (p % 2 = 1) ans = (fastmul (ans, base) % c; 35 base = (fastmul (base, base )) % c; 36 p = p> 1; 37} 38 return ans; 39} 40 int main () 41 {42 // a ^ x = B (mod c) 43/* LL x, y, mod; 44 cin> x> y> mod; 45 c = mod; 46 a = x; 47 B = y; */48 cin> a> B> c; 49 LL m = ceil (sqrt (c); // You must round up to 50 mp. clear (); 51 if (a % c = 0) 52 {53 printf ("-1 \ n"); 54 return 0; 55} 56 // solution condition 57 LL ans of the ferma small theorem; // store the result of each enumeration B * a ^ j58 for (LL j = 0; j <= m; j ++) // a ^ (I * m) = B * a ^ j59 {60 if (j = 0) 61 {62 ans = B % c; 63 mp [ans] = j; // process a ^ 0 = 1 64 continue; 65} 66 ans = (fastmul (ans, a) % c; // a ^ j 67 mp [ans] = j; // store the result of each enumeration 68} 69 LL t = fastpow (a, m, c); 70 ans = 1; // a ^ (I * m) 71 LL flag = 0; 72 for (LL I = 1; I <= m; I ++) 73 {74 ans = (fastmul (ans, t) % c; 75 if (mp [ans]) 76 {77 LL out = fastmul (I, m)-mp [ans]; // x = I * m-j78 printf ("% lld \ n", (out % c + c) % c); 79 flag = 1; 80 break; 81} 82 83} 84 if (! Flag) 85 printf ("-1 \ n"); 86 return 0; 87}AC used