From 60991f8e72c4fb2cfa7440fdaf92a849ab15a0ff Mon Sep 17 00:00:00 2001
From: Linkus000 <linkus@openmailbox.org>
Date: Thu, 16 Dec 2021 22:20:40 +0100
Subject: [PATCH] Primitive root

---
 primitive_root.cpp | 89 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 89 insertions(+)
 create mode 100644 primitive_root.cpp

diff --git a/primitive_root.cpp b/primitive_root.cpp
new file mode 100644
index 0000000..c762527
--- /dev/null
+++ b/primitive_root.cpp
@@ -0,0 +1,89 @@
+#include <bits/stdc++.h>
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+#define pb push_back
+#define mp make_pair
+#define all(a) begin(a),end(a)
+#define FOR(x,val,to) for(int x=(val);x<int((to));++x)
+#define FORE(x,val,to) for(auto x=(val);x<=(to);++x)
+#define FORR(x,arr) for(auto &x: arr)
+#define FORS(x,plus,arr) for(auto x = begin(arr)+(plus); x != end(arr); ++x)
+#define FORREV(x,plus,arr) for(auto x = (arr).rbegin()+(plus); x !=(arr).rend(); ++x)
+#define REE(s_) {cout<<s_<<'\n';exit(0);}
+#define GET(arr) for(auto &i: (arr)) sc(i)
+#define whatis(x) cerr << #x << " is " << (x) << endl;
+#define e1 first
+#define e2 second
+#define INF 0x7f7f7f7f
+typedef std::pair<int,int> pi;
+typedef std::vector<int> vi;
+typedef std::vector<std::string> vs;
+typedef int64_t ll;
+typedef uint64_t ull;
+#define umap unordered_map
+#define uset unordered_set
+using namespace std;
+using namespace __gnu_pbds;
+
+#ifdef ONLINE_JUDGE
+#define whatis(x) ;
+#endif
+#ifdef _WIN32
+#define getchar_unlocked() _getchar_nolock()
+#define _CRT_DISABLE_PERFCRIT_LOCKS
+#endif
+template<class L, class R> ostream& operator<<(ostream &os, map<L, R> P) { for(auto const &vv: P)os<<"("<<vv.first<<","<<vv.second<<")"; return os; }
+template<class T> ostream& operator<<(ostream &os, set<T> V) { os<<"[";for(auto const &vv:V)os<<vv<<","; os<<"]"; return os; }
+template<class T> ostream& operator<<(ostream &os, vector<T> V) { os<<"[";for(auto const &vv:V)os<<vv<<","; os<<"]"; return os; }
+template<class L, class R> ostream& operator<<(ostream &os, pair<L, R> P) { os<<"("<<P.first<<","<<P.second<<")"; return os; }
+inline int fstoi(const string &str){auto it=str.begin();bool neg=0;int num=0;if(*it=='-')neg=1;else num=*it-'0';++it;while(it<str.end()) num=num*10+(*it++-'0');if(neg)num*=-1;return num;}
+inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}}
+inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}}
+template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); }
+template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound
+template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
+#define N 1000001
+
+
+// Primitive root modulo n exists if and only if:
+// n is 1, 2, 4, or
+// n is power of an odd prime number (n=p^k), or
+// n is twice power of an odd prime number (n=2*p^k).
+// https://cp-algorithms.com/algebra/primitive-root.html
+// The following code assumes that the modulo p is a prime number. To make it works for any value of p, we must add calculation of ϕ(p).
+int powmod (int a, int b, int p) {
+    int res = 1;
+    while (b)
+        if (b & 1)
+            res = int (res * 1ll * a % p),  --b;
+        else
+            a = int (a * 1ll * a % p),  b >>= 1;
+    return res;
+}
+
+int generator (int p) {
+    vector<int> fact;
+    int phi = p-1,  n = phi;
+    for (int i=2; i*i<=n; ++i)
+        if (n % i == 0) {
+            fact.push_back (i);
+            while (n % i == 0)
+                n /= i;
+        }
+    if (n > 1)
+        fact.push_back (n);
+
+    for (int res=2; res<=p; ++res) {
+        bool ok = true;
+        for (size_t i=0; i<fact.size() && ok; ++i)
+            ok &= powmod (res, phi / fact[i], p) != 1;
+        if (ok)  return res;
+    }
+    return -1;
+}
+
+int main(){
+    ios_base::sync_with_stdio(0);cin.tie(0);
+    whatis(generator(200003))
+}
+