Problem:
Score: 500 points

Problem Statement

Does there exist an undirected graph with N vertices satisfying the following conditions?

The graph is simple and connected.

The vertices are numbered 1, 2, ..., N.

Let M be the number of edges in the graph. The edges are numbered 1, 2, ..., M, the length of each edge is 1, and Edge i connects Vertex u_i and Vertex v_i.

There are exactly K pairs of vertices (i,\ j)\ (i < j) such that the shortest distance between them is 2.

If there exists such a graph, construct an example.

Constraints

All values in input are integers.

2 \leq N \leq 100

0 \leq K \leq \frac{N(N - 1)}{2}

Input

Input is given from Standard Input in the following format:

N K

Output

If there does not exist an undirected graph with N vertices satisfying the conditions, print -1.

If there exists such a graph, print an example in the following format (refer to Problem Statement for what the symbols stand for):

M
u_1 v_1
:
u_M v_M

If there exist multiple graphs satisfying the conditions, any of them will be accepted.

Sample Input 1

5 3

Sample Output 1

5
4 3
1 2
3 1
4 5
2 3

This graph has three pairs of vertices such that the shortest distance between them is 2: (1,\ 4), (2,\ 4), and (3,\ 5). Thus, the condition is satisfied.

Sample Input 2

5 8

Sample Output 2

-1

There is no graph satisfying the conditions.

Solution in C (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>

int main()
{
    long long n, k;
    long long graph[105][105];
    long long maxv;
    long long edge = 0;

    scanf("%d %d", &n, &k);

    maxv = (n - 1) * (n - 2) / 2;

    if (maxv < k) {
        printf("-1\n");
        return 0;
    }

    for (long long i = 2; i <= n; i++) {
        graph[1][i] = 1;
        edge++;
    }

    long long i = 2;
    while (maxv > k) {
        for (long long j = i + 1; j <= n && maxv > k; j++) {
            graph[i][j] = 1;
            edge++;
            maxv--;
        }
        i++;
    }

    printf("%d\n", edge);
    for (long long i = 1; i <= n; i++) {
        for (long long j = 1; j <= n; j++) {
            if (graph[i][j]) {
                printf("%d %d\n", i, j);
            }
        }
    }

    return 0;
}