Problem: You are given two integers b and w. You have a chessboard of size 10^9 × 10^9 with the top left cell at (1; 1), the cell (1; 1) is painted white.

Your task is to find a connected component on this chessboard that contains exactly b black cells and exactly w white cells. Two cells are called connected if they share a side (i.e. for the cell (x, y) there are at most four connected cells: (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)). A set of cells is called a connected component if for every pair of cells C_1 and C_2 from this set, there exists a sequence of cells c_1, c_2, ..., c_k such that c_1 = C_1, c_k = C_2, all c_i from 1 to k are belong to this set of cells and for every i ∈ [1, k - 1], cells c_i and c_{i + 1} are connected.

Obviously, it can be impossible to find such component. In this case print "NO". Otherwise, print "YES" and any suitable connected component.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 10^5) — the number of queries. Then q queries follow.

The only line of the query contains two integers b and w (1 ≤ b, w ≤ 10^5) — the number of black cells required and the number of white cells required.

It is guaranteed that the sum of numbers of cells does not exceed 2 ⋅ 10^5 (∑ w + ∑ b ≤ 2 ⋅ 10^5).

Output

For each query, print the answer to it.

If it is impossible to find the required component, print "NO" on the first line.

Otherwise, print "YES" on the first line. In the next b + w lines print coordinates of cells of your component in any order. There should be exactly b black cells and w white cells in your answer. The printed component should be connected.

If there are several answers, you can print any. All coordinates in the answer should be in the range [1; 10^9].

Example

Input


3
1 1
1 4
2 5


Output


YES
2 2
1 2
YES
2 3
1 3
3 3
2 2
2 4
YES
2 3
2 4
2 5
1 3
1 5
3 3
3 5

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {

    private static PrintWriter out;

    private static <T> void mprintln(T... ar) {
        for (T i : ar) {
            out.print(i + " ");
        }
        out.println();
    }

    public static void main(String[] args) throws FileNotFoundException {

        // Input from file
        // File inputFile = new File("JavaFile.txt");
        // File outputFile = new File("JavaOutputFile.txt");
        // FileReader fileReader = new FileReader(inputFile);
        // Here it ends

        MyScanner sc = new MyScanner();
        // MyScanner sc = new MyScanner(fileReader);

        out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console
        // out = new PrintWriter(new PrintStream(outputFile)); // Output to file

        getAns(sc);

        out.close();
    }

    /*
     *Don't use builtin function (Math.ceil)
     */

    static final long MOD = (long) (1e9 + 7);

    private static void getAns(MyScanner sc) {
        int t = sc.ni();
        int MAX = (int) 1e5, MIN = (int) -1e5;
        while (t-- > 0) {
            int b = sc.ni(), w = sc.ni();

            if (w > 3 * b + 1 || b > 3 * w + 1) {
                out.println("NO");
                continue;
            }

            out.println("YES");
            int X = (int) 1e6, Y = (int) 1e6;

            if (b < w) {
                int blacks = b;
                int y = Y + 1, x = X;
                mprintln(X, Y);
                w -= b + 1;
                while (b-- > 0) {
                    mprintln(x, y++);
                    mprintln(x, y++);
                }

                x = X + 1;
                y = Y + 1;
                b = blacks;
                while (b-- > 0 && w-- > 0) {
                    mprintln(x, y);
                    y += 2;
                }

                b = blacks;
                x = X - 1;
                y = Y + 1;
                while (b-- > 0 && w-- > 0) {
                    mprintln(x, y);
                    y += 2;
                }
            } else if (b > w){
                int white = w;
                int x = X, y = Y;
                mprintln(X, Y - 1);
                b -= w + 1;
                while (w-- > 0) {
                    mprintln(x, y++);
                    mprintln(x, y++);
                }

                x = X + 1;
                y = Y;
                w = white;
                while (w-- > 0 && b-- > 0) {
                    mprintln(x, y);
                    y += 2;
                }

                x = X - 1;
                y = Y;
                w = white;
                while (w-- > 0 && b-- > 0) {
                    mprintln(x, y);
                    y += 2;
                }
            } else {
                while (w-- > 0) {
                    mprintln(X, Y++);
                    mprintln(X, Y++);
                }
            }
        }
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

        MyScanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }

        MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nn() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            String ans = "";
            try {
                ans = br.readLine();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return ans;
        }

        char nc() {
            return nn().charAt(0);
        }

        int ni() {
            return Integer.parseInt(nn());
        }

        long nl() {
            return Long.parseLong(nn());
        }

        double nd() {
            return Double.parseDouble(nn());
        }

        int[] niArr0(int n) {
            int[] ar = new int[n];
            for (int i = 0; i < n; i++) {
                ar[i] = ni();
            }
            return ar;
        }

        int[] niArr1(int n) {
            int[] ar = new int[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = ni();
            }
            return ar;
        }

        long[] nlArr0(int n) {
            long[] ar = new long[n];
            for (int i = 0; i < n; i++) {
                ar[i] = nl();
            }
            return ar;
        }

        long[] nlArr1(int n) {
            long[] ar = new long[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = nl();
            }
            return ar;
        }
    }
}