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.math.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
import static java.util.Comparator.*;

public class Main {
    FastScanner in;
    PrintWriter out;
    boolean multitests = true;
    long mod = (long) 1e9 + 7; // 998_244_353L || (long) 1e9 + 9
    ArrayList<Integer>[] graph;
    ArrayList<GraphPair>[] weightedGraph;

    private void solve() throws IOException {
        // solveA();
        // solveB();
        // solveC();
        // solveD();
        solveE();
        // solveF();
    }

    private void solveA() throws IOException {
        long[] a = in.nextLongArray(3);
        out.println(sumLong(a) / 2);
    }

    private void solveB() throws IOException {
        int n = in.nextInt(), k = in.nextInt();
        long[] a = in.nextLongArray(n);
        int[] ans = new int[k];
        int s = 0;
        long sum = sumLong(a);
        for (int i = 0; i < n && s < k - 1; i++) {
            if (a[i] % 2 == 1)
                ans[s++] = i + 1;
            sum -= a[i];
        }
        if (sum % 2 == 1)
            ans[s++] = n;
        out.println(s == k ? "YES" : "NO");
        if (s == k) {
            for (int i : ans)
                out.print(i + " ");
            out.println();
        }
    }

    private void solveC() throws IOException {
        int n = in.nextInt();
        int maxX = (int) 1e5, minX = -(int) 1e5;
        int maxY = (int) 1e5, minY = -(int) 1e5;
        for (int i = 0; i < n; i++) {
            int x = in.nextInt(), y = in.nextInt();
            if (in.nextInt() == 0)
                minX = max(minX, x);
            if (in.nextInt() == 0)
                maxY = min(maxY, y);
            if (in.nextInt() == 0)
                maxX = min(maxX, x);
            if (in.nextInt() == 0)
                minY = max(minY, y);
        }
        out.println(minX <= maxX && minY <= maxY ? "1 " + minX + " " + minY : "0");
    }

    private void solveD() throws IOException {
        int n = in.nextInt(), k = in.nextInt();
        char[] s = in.next().toCharArray(), t = "RGB".toCharArray();
        int ans = k;
        for (int i = 0; i < t.length; i++) {
            int[] pref = new int[n];
            for (int j = 0; j < n; j++)
                pref[j] = (j == 0 ? 0 : pref[j - 1]) + (s[j] == t[(i + j) % 3] ? 0 : 1);
            for (int j = k - 1; j < n; j++)
                ans = min(ans, pref[j] - (j < k ? 0 : pref[j - k]));
        }
        out.println(ans);
    }

    private void solveE() throws IOException {
        int b = in.nextInt(), w = in.nextInt();

        if (min(b, w) * 3 + 1 < max(b, w)) {
            out.println("NO");
            return;
        }

        out.println("YES");

        int sx = 3, sy = w > b ? 1 : 2;
        if (w < b) {
            int orange = w;
            w = b;
            b = orange;
        }

        if (w > b) {
            int x = sx, y = sy;
            out.println(x + " " + y);
            w--;
            while (w > b) {
                y++;
                out.println(x + " " + y);
                b--;
                out.println(x - 1 + " " + y);
                out.println(x + 1 + " " + y);
                w -= 2;
                if (w > b) {
                    y++;
                    out.println(x + " " + y);
                    w--;
                }
            }
        }

        if (w != b)
            b = 1 / 0;

        int x = sx, y = sy;
        while (b > 0) {
            x++;
            out.println(x + " " + y);
            x++;
            out.println(x + " " + y);
            b--;
        }
    }

    private void solveF() throws IOException {

    }

    void shuffleInt(int[] a) {
        Random random = new Random();
        for (int i = a.length - 1; i > 0; i--) {
            int j = random.nextInt(i + 1);
            int swap = a[j];
            a[j] = a[i];
            a[i] = swap;
        }
    }

    void shuffleLong(long[] a) {
        Random random = new Random();
        for (int i = a.length - 1; i > 0; i--) {
            int j = random.nextInt(i + 1);
            long swap = a[j];
            a[j] = a[i];
            a[i] = swap;
        }
    }

    void reverseInt(int[] a) {
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            int swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }
    }

    void reverseLong(long[] a) {
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            long swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }
    }

    int maxInt(int[] a) {
        int max = a[0];
        for (int i = 1; i < a.length; i++)
            if (max < a[i])
                max = a[i];
        return max;
    }

    long maxLong(long[] a) {
        long max = a[0];
        for (int i = 1; i < a.length; i++)
            if (max < a[i])
                max = a[i];
        return max;
    }

    int minInt(int[] a) {
        int min = a[0];
        for (int i = 1; i < a.length; i++)
            if (min > a[i])
                min = a[i];
        return min;
    }

    long minLong(long[] a) {
        long min = a[0];
        for (int i = 1; i < a.length; i++)
            if (min > a[i])
                min = a[i];
        return min;
    }

    long sumInt(int[] a) {
        long s = 0;
        for (int i = 0; i < a.length; i++)
            s += a[i];
        return s;
    }

    long sumLong(long[] a) {
        long s = 0;
        for (int i = 0; i < a.length; i++)
            s += a[i];
        return s;
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long binpowmod(long a, long n) {
        long res = 1;
        a %= mod;
        n %= mod - 1;
        while (n > 0) {
            if (n % 2 == 1)
                res = (res * a) % mod;
            a = (a * a) % mod;
            n /= 2;
        }
        return res;
    }

    class GraphPair implements Comparable<GraphPair> {
        int v;
        long w;

        GraphPair(int v, long w) {
            this.v = v;
            this.w = w;
        }

        public int compareTo(GraphPair o) {
            return w != o.w ? Long.compare(w, o.w) : Integer.compare(v, o.v);
        }
    }

    ArrayList<Integer>[] createGraph(int n) throws IOException {
        ArrayList<Integer>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<>();
        return graph;
    }

    ArrayList<GraphPair>[] createWeightedGraph(int n) throws IOException {
        ArrayList<GraphPair>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<>();
        return graph;
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s), 32768);
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

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

        int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextInt();
            return a;
        }

        int[][] nextIntTable(int n, int m) throws IOException {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = in.nextInt();
            return a;
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextLong();
            return a;
        }

        long[][] nextLongTable(int n, int m) throws IOException {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = in.nextLong();
            return a;
        }

        ArrayList<Integer>[] nextGraph(int n, int m, boolean directed) throws IOException {
            ArrayList<Integer>[] graph = createGraph(n);
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1, u = in.nextInt() - 1;
                graph[v].add(u);
                if (!directed)
                    graph[u].add(v);
            }
            return graph;
        }

        ArrayList<GraphPair>[] nextWeightedGraph(int n, int m, boolean directed) throws IOException {
            ArrayList<GraphPair>[] graph = createWeightedGraph(n);
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1, u = in.nextInt() - 1;
                long w = in.nextLong();
                graph[v].add(new GraphPair(u, w));
                if (!directed)
                    graph[u].add(new GraphPair(v, w));
            }
            return graph;
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }
    }

    private void run() throws IOException {
        in = new FastScanner(System.in); // new FastScanner(new FileInputStream(".in"));
        out = new PrintWriter(System.out); // new PrintWriter(new FileOutputStream(".out"));

        for (int t = multitests ? in.nextInt() : 1; t-- > 0; )
            solve();

        out.flush();
        out.close();
    }

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