#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline bool upmin(T &x, T y) {
  return y < x ? x = y, 1 : 0;
}
template <typename T>
inline bool upmax(T &x, T y) {
  return x < y ? x = y, 1 : 0;
}
const long double eps = 1e-9;
const long double pi = acos(-1);
const int oo = 1 << 30;
const long long loo = 1ll << 60;
const int mods = 1e9 + 7;
const int MAXN = 500005;
const int INF = 0x3f3f3f3f;
namespace FastIO {
constexpr int SIZE = (1 << 21) + 1;
int num = 0, f;
char ibuf[SIZE], obuf[SIZE], que[65], *iS, *iT, *oS = obuf,
                                                *oT = obuf + SIZE - 1, c;
inline void flush() {
  fwrite(obuf, 1, oS - obuf, stdout);
  oS = obuf;
}
inline void putc(char c) {
  *oS++ = c;
  if (oS == oT) flush();
}
inline void getc(char &c) {
  for (c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                       (iS == iT ? EOF : *iS++))
                     : *iS++);
       !isalpha(c) && c != EOF;
       c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    ;
}
inline void reads(char *st) {
  char c;
  int n = 0;
  getc(st[++n]);
  for (c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                       (iS == iT ? EOF : *iS++))
                     : *iS++);
       isalpha(c);
       c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    st[++n] = c;
  st[++n] = '\0';
}
template <class I>
inline void read(I &x) {
  for (f = 1, c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                              (iS == iT ? EOF : *iS++))
                            : *iS++);
       c < '0' || c > '9';
       c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    if (c == '-') f = -1;
  for (x = 0; c >= '0' && c <= '9';
       c = (iS == iT ? (iT = ((iS = ibuf) + fread(ibuf, 1, SIZE, stdin)),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    x = (x << 3) + (x << 1) + (c & 15);
  x *= f;
}
template <class I>
inline void print(I x) {
  if (x < 0) putc('-'), x = -x;
  if (!x) putc('0');
  while (x) que[++num] = x % 10 + 48, x /= 10;
  while (num) putc(que[num--]);
}
inline void putstr(string st) {
  for (int i = 0; i < (int)st.size(); ++i) putc(st[i]);
}
struct Flusher_ {
  ~Flusher_() { flush(); }
} io_Flusher_;
}  // namespace FastIO
using FastIO ::print;
using FastIO ::putc;
using FastIO ::putstr;
using FastIO ::read;
using FastIO ::reads;
vector<int> V[MAXN], e[MAXN], Ans;
int fa[MAXN], dep[MAXN];
void dfs(int x, int father) {
  fa[x] = father;
  dep[x] = dep[father] + 1;
  V[dep[x]].push_back(x);
  for (auto v : e[x]) {
    if (dep[v]) continue;
    dfs(v, x);
  }
}
signed main() {
  int Case;
  read(Case);
  while (Case--) {
    int n, m;
    Ans.clear();
    read(n), read(m);
    for (int i = 1; i <= n; ++i) V[i].clear(), e[i].clear(), dep[i] = 0;
    for (int i = 1, u, v; i <= m; ++i)
      read(u), read(v), e[u].push_back(v), e[v].push_back(u);
    dfs(1, 0);
    for (int i = 1; i <= n; ++i)
      if (dep[i] >= (n - 1) / 2 + 1) {
        putstr(string("PATH\n"));
        int x = i;
        while (x) Ans.push_back(x), x = fa[x];
        print(Ans.size()), putc('\n');
        for (auto v : Ans) print(v), putc(' ');
        putc('\n');
        break;
      }
    if (Ans.size()) continue;
    for (int i = 1; i <= n; ++i)
      for (int j = 0; j + 1 < (int)V[i].size(); j += 2)
        Ans.push_back(V[i][j]), Ans.push_back(V[i][j + 1]);
    putstr(string("PAIRING\n"));
    print(Ans.size() / 2), putc('\n');
    for (int i = 0; i + 1 < (int)Ans.size(); i += 2)
      print(Ans[i]), putc(' '), print(Ans[i + 1]), putc('\n');
  }
  return 0;
}
