Problem: 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

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

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.

Examples

Input

7 3 3
2 3 1


Output

7
1 3
2 1
2 6
2 4
7 4
3 5


Input

14 5 6
4 4 2 2 1


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


Input

3 1 1
2


Output

-1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.Collection;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author An Almost Retired Guy
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskG solver = new TaskG();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskG {
        int[] A;
        int[] parent;
        EzIntArrayList[] level;
        EzIntArrayList[] children;
        int id = 0;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt(), t = in.nextInt(), k = in.nextInt();
            t++;
            A = new int[t + 1];
            A[0] = 1;
            for (int i = 1; i < t; i++) A[i] = in.nextInt();
            level = new EzIntArrayList[t];
            children = new EzIntArrayList[n];
            for (int i = 0; i < t; i++) level[i] = new EzIntArrayList();
            for (int i = 0; i < n; i++) children[i] = new EzIntArrayList();
            parent = new int[n];
            for (int i = 0; i < t; i++)
                while (A[i] > 0) {
                    int p = -1;
                    if (i > 0) {
                        assert (!level[i - 1].isEmpty());
                        p = level[i - 1].get(0);
                        children[p].add(id);
                    }
                    dfs(id++, i, p);
                }
            for (int i = 1; i < n; i++) if (children[i].isEmpty()) k--;
            if (k < 0) {
                out.println(-1);
                return;
            }
            for (int i = 1; i < t; i++)
                for (int j = 1; j < level[i].size(); j++) {
                    if (k == 0) continue;
                    int u = level[i].get(j), begin = level[i].get(0);
                    if (children[u].isEmpty()) continue;
                    k--;
                    for (int v : children[u].toArray()) {
                        parent[v] = begin;
                        children[begin].add(v);
                    }
                    children[u].clear();
                }
            if (k > 0) out.println(-1);
            else {
                out.println(n);
                for (int i = 1; i < n; i++) out.println((i + 1) + " " + (parent[i] + 1));
            }
        }

        void dfs(int u, int h, int p) {
            parent[u] = p;
            level[h].add(u);
            A[h]--;
            if (A[h + 1] > 0) {
                children[u].add(id);
                dfs(id++, h + 1, u);
            }
        }

    }

    static final class PrimitiveHashCalculator {
        private PrimitiveHashCalculator() {
        }

        public static int getHash(int x) {
            return x;
        }

    }

    static interface EzIntList extends EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(new BufferedOutputStream(outputStream));
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public void close() {
            super.close();
        }

    }

    static class EzIntArrayList implements EzIntList, EzIntStack {
        private static final int DEFAULT_CAPACITY = 10;
        private static final double ENLARGE_SCALE = 2.0;
        private static final int HASHCODE_INITIAL_VALUE = 0x811c9dc5;
        private static final int HASHCODE_MULTIPLIER = 0x01000193;
        private int[] array;
        private int size;

        public EzIntArrayList() {
            this(DEFAULT_CAPACITY);
        }

        public EzIntArrayList(int capacity) {
            if (capacity < 0) {
                throw new IllegalArgumentException("Capacity must be non-negative");
            }
            array = new int[capacity];
            size = 0;
        }

        public EzIntArrayList(EzIntCollection collection) {
            size = collection.size();
            array = new int[size];
            int i = 0;
            for (EzIntIterator iterator = collection.iterator(); iterator.hasNext(); ) {
                array[i++] = iterator.next();
            }
        }

        public EzIntArrayList(int[] srcArray) {
            size = srcArray.length;
            array = new int[size];
            System.arraycopy(srcArray, 0, array, 0, size);
        }

        public EzIntArrayList(Collection<Integer> javaCollection) {
            size = javaCollection.size();
            array = new int[size];
            int i = 0;
            for (int element : javaCollection) {
                array[i++] = element;
            }
        }


        public int size() {
            return size;
        }


        public boolean isEmpty() {
            return size == 0;
        }


        public EzIntIterator iterator() {
            return new EzIntArrayListIterator();
        }


        public int[] toArray() {
            int[] result = new int[size];
            System.arraycopy(array, 0, result, 0, size);
            return result;
        }


        public boolean add(int element) {
            if (size == array.length) {
                enlarge();
            }
            array[size++] = element;
            return true;
        }


        public void clear() {
            size = 0;
        }


        public int get(int index) {
            if (index < 0 || index >= size) {
                throw new IndexOutOfBoundsException("Index " + index + " is out of range, size = " + size);
            }
            return array[index];
        }

        private void enlarge() {
            int newSize = Math.max(size + 1, (int) (size * ENLARGE_SCALE));
            int[] newArray = new int[newSize];
            System.arraycopy(array, 0, newArray, 0, size);
            array = newArray;
        }


        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            EzIntArrayList that = (EzIntArrayList) o;

            if (size != that.size) {
                return false;
            }
            for (int i = 0; i < size; i++) {
                if (array[i] != that.array[i]) {
                    return false;
                }
            }
            return true;
        }


        public int hashCode() {
            int hash = HASHCODE_INITIAL_VALUE;
            for (int i = 0; i < size; i++) {
                hash = (hash ^ PrimitiveHashCalculator.getHash(array[i])) * HASHCODE_MULTIPLIER;
            }
            return hash;
        }


        public String toString() {
            StringBuilder sb = new StringBuilder();
            sb.append('[');
            for (int i = 0; i < size; i++) {
                sb.append(array[i]);
                if (i < size - 1) {
                    sb.append(", ");
                }
            }
            sb.append(']');
            return sb.toString();
        }

        private class EzIntArrayListIterator implements EzIntIterator {
            private int curIndex = 0;


            public boolean hasNext() {
                return curIndex < size;
            }


            public int next() {
                if (curIndex == size) {
                    throw new NoSuchElementException("Iterator doesn't have more elements");
                }
                return array[curIndex++];
            }

        }

    }

    static interface EzIntIterator {
        boolean hasNext();

        int next();

    }

    static interface EzIntStack extends EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static interface EzIntCollection {
        int size();

        EzIntIterator iterator();

        boolean equals(Object object);

        int hashCode();

        String toString();

    }

    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

    }
}