#include <bits/stdc++.h>   using namespace std;   const int N = 500000;   int n, m;   vector<int> nei[N + 1];   bool vis[N + 1];   int fa[N + 1], dep[N + 1];   void dfs(int x = 1) {     vis[x] = true;     for (int i = 0; i < nei[x].size(); i++) {       int y = nei[x][i];       if (vis[y]) continue;       fa[y] = x;       dep[y] = dep[x] + 1;       dfs(y);     }   }   vector<int> buc[N + 1];   void mian() {     scanf( %d%d , &n, &m);     for (int i = 1; i <= n; i++)       nei[i].clear(), buc[i].clear(), vis[i] = fa[i] = dep[i] = 0;     while (m--) {       int x, y;       scanf( %d%d , &x, &y);       nei[x].push_back(y);       nei[y].push_back(x);     }     dep[1] = 1;     dfs();     for (int i = 1; i <= n; i++)       if (dep[i] >= n + 1 >> 1) {         puts( PATH );         printf( %d n , dep[i]);         while (i) printf( %d  , i), i = fa[i];         puts(  );         return;       } else         buc[dep[i]].push_back(i);     puts( PAIRING );     int cnt = 0;     for (int i = 1; i <= n; i++) cnt += buc[i].size() >> 1;     printf( %d n , cnt);     for (int i = 1; i <= n; i++) {       for (int j = 0; j + 1 < buc[i].size(); j += 2)         printf( %d %d n , buc[i][j], buc[i][j + 1]);     }   }   int main() {     int testnum;     cin >> testnum;     while (testnum--) mian();     return 0;   }   