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>
#include<stdint.h>
#include<inttypes.h>

typedef int32_t i32;

void run (void) {
  i32 n, k;
  scanf ("%" SCNi32 "%" SCNi32, &n, &k);
  if (k > (n - 1) * (n - 2) / 2) {
    puts ("-1");
    return;
  }
  i32 cnt = n - 1 + ((n - 1) * (n - 2) / 2 - k);
  printf ("%" PRIi32 "\n", cnt);
  for (i32 i = 1; i < n; ++i) {
    printf ("%" PRIi32 " %" PRIi32 "\n", 1, i + 1);
  }
  i32 t = (n - 1) * (n - 2) / 2 - k;
  for (i32 i = 1; t > 0; ++i) {
    for (i32 j = i + 1; j < n && t > 0; ++j, --t) {
      printf ("%" PRIi32 " %" PRIi32 "\n", i + 1, j + 1);
    }
  }
}

int main (void) {
  run();
  return 0;
}