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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

struct vector{int a; int b;};

int main(void) {
    int i, n, k, l, p, q, m;
    scanf("%d %d", &n, &k);
    if(k > (n-1)*(n-2)/2){printf("-1\n"); return 0;}
    struct vector v[n*(n-1)/2];
    for(i = 0; i < n-1; ++i){
        v[i].a = 1; v[i].b = i+2;
    }
    p = 2; q = 3;
    for(l = (n-1)*(n-2)/2; l > k; ++i, ++q, --l){
        v[i].a = p; v[i].b = q;
        if(q >= n){++p; q = p;}
    }
    m = i;
    printf("%d\n", m);
    for(i = 0; i < m; ++i){
        printf("%d %d\n", v[i].a, v[i].b);
    }
    return 0;
}