Problem: You are given a permutation a_1, a_2, ..., a_n of numbers from 1 to n. Also, you have n sets S_1,S_2,..., S_n, where S_i=\\{a_i\}. Lastly, you have a variable cnt, representing the current number of sets. Initially, cnt = n.

We define two kinds of functions on sets:

f(S)=min_{u∈ S} u;

g(S)=max_{u∈ S} u.

You can obtain a new set by merging two sets A and B, if they satisfy g(A)<f(B) (Notice that the old sets do not disappear).

Formally, you can perform the following sequence of operations:

  * cnt← cnt+1;

  * S_{cnt}=S_u∪ S_v, you are free to choose u and v for which 1≤ u, v < cnt and which satisfy g(S_u)<f(S_v).




You are required to obtain some specific sets.

There are q requirements, each of which contains two integers l_i,r_i, which means that there must exist a set S_{k_i} (k_i is the ID of the set, you should determine it) which equals \\{a_u∣ l_i≤ u≤ r_i\}, which is, the set consisting of all a_i with indices between l_i and r_i.

In the end you must ensure that cnt≤ 2.2× 10^6. Note that you don't have to minimize cnt. It is guaranteed that a solution under given constraints exists.

Input

The first line contains two integers n,q (1≤ n ≤ 2^{12},1 ≤ q ≤ 2^{16}) — the length of the permutation and the number of needed sets correspondently.

The next line consists of n integers a_1,a_2,⋅⋅⋅, a_n (1≤ a_i≤ n, a_i are pairwise distinct) — given permutation.

i-th of the next q lines contains two integers l_i,r_i (1≤ l_i≤ r_i≤ n), describing a requirement of the i-th set.

Output

It is guaranteed that a solution under given constraints exists.

The first line should contain one integer cnt_E (n≤ cnt_E≤ 2.2× 10^6), representing the number of sets after all operations.

cnt_E-n lines must follow, each line should contain two integers u, v (1≤ u, v≤ cnt', where cnt' is the value of cnt before this operation), meaning that you choose S_u, S_v and perform a merging operation. In an operation, g(S_u)<f(S_v) must be satisfied.

The last line should contain q integers k_1,k_2,⋅⋅⋅,k_q (1≤ k_i≤ cnt_E), representing that set S_{k_i} is the ith required set.

Please notice the large amount of output.

Examples

Input


3 2
1 3 2
2 3
1 3


Output


6
3 2
1 3
5 2
4 6 

Input


2 4
2 1
1 2
1 2
1 2
1 1


Output


5
2 1
2 1
2 1
5 3 3 1

Note

In the first sample:

We have S_1=\{1\},S_2=\{3\},S_3=\{2\} initially.

In the first operation, because g(S_3)=2<f(S_2)=3, we can merge S_3,S_2 into S_4=\{2,3\}.

In the second operation, because g(S_1)=1<f(S_3)=2, we can merge S_1,S_3 into S_5=\{1,2\}.

In the third operation, because g(S_5)=2<f(S_2)=3, we can merge S_5,S_2 into S_6=\{1,2,3\}.

For the first requirement, S_4=\{2,3\}=\\{a_2,a_3\}, satisfies it, thus k_1=4.

For the second requirement, S_6=\{1,2,3\}=\\{a_1,a_2,a_3\}, satisfies it, thus k_2=6

Notice that unused sets, identical sets, outputting the same set multiple times, and using sets that are present initially are all allowed.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int w = 0, x = 0;
  char c = getchar();
  while (!isdigit(c)) w |= c == '-', c = getchar();
  while (isdigit(c)) x = x * 10 + (c ^ 48), c = getchar();
  return w ? -x : x;
}
namespace star {
const int maxn = (1 << 12) + 5, siz = 1 << 8;
int n, m, N, a[maxn], pos[maxn], cnt, ans[2200005];
pair<int, int> c[(1 << 22) + 5];
struct Set {
  vector<int> val;
  vector<vector<int>> id;
  void init(int x) {
    val.resize(x), id.resize(x);
    for (int i = 0; i < x; i++) id[i].resize(x - i);
  }
  Set() {}
  Set(int x) {
    init(1);
    val[0] = pos[x], id[0][0] = pos[x];
  }
  int query(int l, int r) {
    if (r < val.front() or l > val.back()) return 0;
    l = lower_bound(val.begin(), val.end(), l) - val.begin();
    r = upper_bound(val.begin(), val.end(), r) - val.begin() - 1;
    return l <= r ? id[l][r - l] : 0;
  }
} b[maxn / siz + 5];
int merge(int x, int y) {
  if (!x or !y) return x | y;
  c[++cnt] = make_pair(x, y);
  return cnt;
}
Set update(Set x, Set y) {
  Set res;
  res.init(x.val.size() + y.val.size());
  merge(x.val.begin(), x.val.end(), y.val.begin(), y.val.end(),
        res.val.begin());
  for (int i = 0; i < res.val.size(); i++)
    for (int j = i; j < res.val.size(); j++)
      res.id[i][j - i] = merge(x.query(res.val[i], res.val[j]),
                               y.query(res.val[i], res.val[j]));
  return res;
}
Set solve(int l, int r) {
  if (l == r) return Set(l);
  int mid = l + r >> 1;
  return update(solve(l, mid), solve(mid + 1, r));
}
inline void work() {
  n = cnt = read(), m = read();
  N = (n - 1) / siz + 1;
  for (int i = 1; i <= n; i++) pos[a[i] = read()] = i;
  for (int i = 1; i <= N; i++) b[i] = solve(siz * (i - 1) + 1, min(siz * i, n));
  for (int i = 1; i <= m; i++) {
    int l = read(), r = read();
    for (int j = 1; j <= N; j++) ans[i] = merge(ans[i], b[j].query(l, r));
  }
  printf("%d\n", cnt);
  for (int i = n + 1; i <= cnt; i++) printf("%d %d\n", c[i].first, c[i].second);
  for (int i = 1; i <= m; i++) printf("%d ", ans[i]);
}
}  // namespace star
signed main() {
  star::work();
  return 0;
}