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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.stream.Stream;

public class Main {

	public static void main(String[] args) throws IOException {
		new Main().solve();
	}

	private void solve() throws IOException {
		try {
			//			solveA();
			//			solveB();
			//			solveC();
			//			solveD();
			solveE();
			//			 solveF();
		} finally {
			if (in != null) {
				in.close();
			}
			if (out != null) {
				out.flush();
				out.close();
			}
		}

	}

	private void solveA() {
		char[] wk = next().toCharArray();
		for (int i = 1; i < wk.length; i++) {
			if (wk[i] == wk[i - 1]) {
				out.println("Bad");
				return;
			}
		}
		out.println("Good");
	}

	private void solveB() {
		int n = nextInt();
		int l = nextInt();

		int total = 0;
		int temp = Integer.MAX_VALUE;
		for (int i = 1; i <= n; i++) {
			total += l + i - 1;
			if (Math.abs(temp) > Math.abs(l + i - 1)) {
				temp = (l + i - 1);
			}
		}
		out.println(total - temp);
	}

	private void solveC() {
		long a = nextLong();
		long b = nextLong();
		long c = nextLong();
		long d = nextLong();

		long res1 = (b / c) - ((a - 1) / c);
		long res2 = (b / d) - ((a - 1) / d);
		long lcm = getLcm2Args(c, d);
		long res4 = (b / lcm) - ((a - 1) / lcm);

		out.println((b - (a - 1)) - (res1 + res2 - res4));
	}

	public long getLcm2Args(long num1, long num2) {
		return num1 * num2 / getGcd2Args(num1, num2);
	}

	public long getGcd2Args(long num1, long num2) {
		try {
			long wkVal1 = Long.max(num1, num2);
			long wkVal2 = Long.min(num1, num2);
			long res = wkVal1 % wkVal2;
			if (res != 0) {
				return getGcd2Args(wkVal2, res);
			} else {
				return wkVal2;
			}

		} catch (Exception e) {
			System.out.println("num1 : " + num1 + " / num2:" + num2);
			e.printStackTrace();
			return -1;
		}

	}

	private void solveD() {
		int n = nextInt();
		int[][] ab = Stream.generate(() -> new int[] { nextInt(), nextInt() }).limit(n).toArray(int[][]::new);
		Arrays.sort(ab, (x, y) -> {
			if (x[1] < y[1]) {
				return -1;
			} else if (x[1] > y[1]) {
				return 1;
			} else {
				if (x[0] < y[0]) {
					return -1;
				} else if (x[0] > y[0]) {
					return 1;
				} else {
					return 0;
				}
			}
		});
		long curTime = 0;
		for (int i = 0; i < n; i++) {
			curTime += ab[i][0];
			if (curTime > ab[i][1]) {
				out.println("No");
				return;
			}
		}
		out.println("Yes");
	}

	private void solveE() {
		int n = nextInt();
		int k = nextInt();

		/*
		 * Kの下限は0
		 * 完全グラフ（ある頂点から、他の頂点への距離が全て1）
		 *
		 * Kの上限は(n-1)(n-2)/2
		 * star（ある頂点を起点に、ほかの頂点へ辺が伸びている）
		 * 全頂点の組み合わせがn(n-1)/2個
		 * 全体を連結するには、辺を(n-1)本貼る必要がある？
		 *
		 */

		long cntEdge = (n - 1) * (n - 2) / 2;
		if (k > cntEdge) {
			out.println(-1);
			return;
		}

		long maxCnt = cntEdge - k + (n - 1);
		long cnt = 0;
		StringBuilder builder = new StringBuilder();
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= n; j++) {
				if (i == j || i > j) {
					continue;
				}
				if (cnt <= maxCnt) {
					builder.append(i + " " + j + System.lineSeparator());
				}
				cnt++;
			}
		}

		out.println(maxCnt);
		out.println(builder.toString());
	}

	private void solveF() {
		int n = nextInt();

		out.println("");
	}

	private final PrintWriter out = new PrintWriter(System.out);
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private void skipUnprintable() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

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

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
}