1 #include <bits/stdc++.h>
 2 using namespace std;
 3 
 4 typedef long long ll;
 5 int t;
 6 ll n, p;
 7 ll w;
 8 
 9 struct num {  //建立一個複數域
10 
11   ll x, y;
12 };
13 
14 num mul(num a, num b, ll p) {  //複數乘法
15   num ans = {0, 0};
16   ans.x = ((a.x * b.x % p + a.y * b.y % p * w % p) % p + p) % p;
 
17   ans.y = ((a.x * b.y % p + a.y * b.x % p) % p + p) % p;
18   return ans;
19 }
20 
21 ll binpow_real(ll a, ll b, ll p) {  //實部快速冪
22   ll ans = 1;
23   while (b) {
24     if (b & 1) ans = ans * a % p;
25     a = a * a % p;
26     b >>= 1;
27   }
28   return ans % p;
29 }
30 
31 ll binpow_imag(num a, ll b, ll p) {  //
 
虛部快速冪
32   num ans = {1, 0};
33   while (b) {
34     if (b & 1) ans = mul(ans, a, p);
35     a = mul(a, a, p);
36     b >>= 1;
37   }
38   return ans.x % p;
39 }
40 
41 ll cipolla(ll n, ll p) {
42   n %= p;
43   if (p == 2) return n;
44   if (binpow_real(n, (p - 1) / 2, p) == p - 1) return -1
 
;
45   ll a;
46   while (1) {  //生成隨機數再檢驗找到滿足非二次剩餘的a
47     a = rand() % p;
48     w = ((a * a % p - n) % p + p) % p;
49     if (binpow_real(w, (p - 1) / 2, p) == p - 1) break;
50   }
51   num x = {a, 1};
52   return binpow_imag(x, (p + 1) / 2, p);
53 }