New Roads
Contest: Codeforces Round 386 (Div. 2)
Difficulty rating: 2100
Tags: constructive algorithms, graphs, trees

There are n cities in Berland, each of them has a unique id — an integer from 1 to n, the capital is the one with id 1. Now there is a serious problem in Berland with roads — there are no roads.

That is why there was a decision to build n - 1 roads so that there will be exactly one simple path between each pair of cities.

In the construction plan t integers a1, a2, ..., at were stated, where t equals to the distance from the capital to the most distant city, concerning new roads. ai equals the number of cities which should be at the distance i from the capital. The distance between two cities is the number of roads one has to pass on the way from one city to another.

Also, it was decided that among all the cities except the capital there should be exactly k cities with exactly one road going from each of them. Such cities are dead-ends and can't be economically attractive. In calculation of these cities the capital is not taken into consideration regardless of the number of roads from it.

Your task is to offer a plan of road's construction which satisfies all the described conditions or to inform that it is impossible.

Input format:
The first line contains three positive numbers n, t and k (2 ≤ n ≤ 2·105, 1 ≤ t, k < n) — the distance to the most distant city from the capital and the number of cities which should be dead-ends (the capital in this number is not taken into consideration).

The second line contains a sequence of t integers a1, a2, ..., at (1 ≤ ai < n), the i-th number is the number of cities which should be at the distance i from the capital. It is guaranteed that the sum of all the values ai equals n - 1.

Output format:
If it is impossible to built roads which satisfy all conditions, print -1.

Otherwise, in the first line print one integer n — the number of cities in Berland. In the each of the next n - 1 line print two integers — the ids of cities that are connected by a road. Each road should be printed exactly once. You can print the roads and the cities connected by a road in any order.

If there are multiple answers, print any of them. Remember that the capital has id 1.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Example input:
7 3 3
2 3 1

Example output:
7
1 3
2 1
2 6
2 4
7 4
3 5

Example input:
14 5 6
4 4 2 2 1

Example output:
14
3 1
1 4
11 6
1 2
10 13
6 10
10 12
14 12
8 4
5 1
3 7
2 6
5 9

Editorial:
The statement of this problem equals to: we need to build rooted tree with k leafs and for each i from 1 to n on the depth i there are ai vertices.
Let m is sum of all numbers from a — the number of vertices in the tree without root.
At first let build the path from the root to the leaf on the depth n, i. e. on each level we create one vertex which connect with vertex on previous level. In resulting tree we necessarily have such path.
Let c is the number of vertices (do not consider already created vertices) which we need to make "not leafs". It is equals to c = m - k - n + 1.
If now c < 0 there is no answer — we can not make less number of leafs which we already have.
In the other case we need to each level i until c > 0 and on the level i - 1 we have leafs and the level i does not filled we will add new vertex to random vertex from the level i - 1, which does not a leaf. Other vertices on the level i we can add to vertex which has been created when we built path from the root to the depth n.
If on the current step c > 0 — there is no solution. In the other case we built needed tree and can print the answer.