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>
int n, q, a[1 << 13], x[1 << 22], y[1 << 22];
int cid;
int merge(int u, int v) { return x[++cid] = u, y[cid] = v, cid; }
struct block {
  int pos[1 << 9], sz;
  int idx[1 << 9][1 << 9];
  void recurbuild(int L, int R) {
    if (L == R) {
      idx[L][L] = pos[L];
      return;
    }
    int M = (L + R) >> 1;
    recurbuild(L, M), recurbuild(M + 1, R);
    register int i, ii, iii;
    int cur[1 << 9][1 << 9];
    for (i = L; i <= R; i++)
      for (ii = L; ii <= R; ii++)
        if (pos[i] < pos[ii]) {
          int DL = -1, DR = -1, TL = -1, TR = -1;
          for (iii = L; iii <= M; iii++)
            if (pos[iii] <= pos[ii] && pos[iii] >= pos[i]) {
              if (DL < 0) DL = DR = iii;
              if (pos[DL] > pos[iii])
                DL = iii;
              else if (pos[DR] < pos[iii])
                DR = iii;
            }
          for (iii = M + 1; iii <= R; iii++)
            if (pos[iii] <= pos[ii] && pos[iii] >= pos[i]) {
              if (TL < 0) TL = TR = iii;
              if (pos[TL] > pos[iii])
                TL = iii;
              else if (pos[TR] < pos[iii])
                TR = iii;
            }
          if (~DL && ~TL)
            cur[i][ii] = merge(idx[DL][DR], idx[TL][TR]);
          else
            cur[i][ii] = 0;
        }
    for (i = L; i <= R; i++)
      for (ii = L; ii <= R; ii++)
        if (pos[i] < pos[ii])
          if (cur[i][ii]) idx[i][ii] = cur[i][ii];
  }
  void build() {
    for (sz = 0; sz < 255; sz++)
      if (!pos[sz + 1]) break;
    recurbuild(0, sz);
  }
} B[18];
int p[1 << 13], w[1 << 17];
int rebuild(int l, int r) {
  register int i;
  int pl[19], pr[19];
  for (i = 0; i <= 18; i++) pl[i] = pr[i] = -1;
  for (i = l; i <= r; i++) {
    int idb = a[i] >> 8, idt = a[i] & 255;
    if (~pl[idb]) {
      if (B[idb].pos[pl[idb]] > i)
        pl[idb] = idt;
      else if (B[idb].pos[pr[idb]] < i)
        pr[idb] = idt;
    } else
      pl[idb] = pr[idb] = idt;
  }
  int ret = 0;
  for (i = 0; i <= 18; i++)
    if (~pl[i]) {
      if (!ret)
        ret = B[i].idx[pl[i]][pr[i]];
      else
        ret = merge(ret, B[i].idx[pl[i]][pr[i]]);
    }
  return ret;
}
int main() {
  scanf("%d%d", &n, &q), cid = n;
  register int i;
  for (i = 1; i <= n; i++) scanf("%d", a + i), a[i]--;
  for (i = 1; i <= n; i++) p[a[i]] = i, B[a[i] >> 8].pos[a[i] & 255] = i;
  for (i = 0; i <= ((n - 1) >> 8); i++) B[i].build();
  for (i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r), w[i] = rebuild(l, r);
  }
  printf("%d\n", cid);
  for (i = n + 1; i <= cid; i++) printf("%d %d\n", x[i], y[i]);
  for (i = 1; i <= q; i++) printf("%d ", w[i]);
  puts("");
}