The robot is located on a checkered rectangular board of size n × m (n rows, m columns). The rows in the board are numbered from 1 to n from top to bottom, and the columns — from 1 to m from left to right.

The robot is able to move from the current cell to one of the four cells adjacent by side.

The sequence of commands s executed by the robot is given. Each command is denoted by one of the symbols 'L', 'R', 'D' or 'U', and triggers the movement to left, right, down or up, respectively.

The robot can start its movement in any cell. The robot executes the commands starting from the first one, strictly in the order in which they are listed in s. If the robot moves beyond the edge of the board, it falls and breaks. A command that causes the robot to break is not considered successfully executed.

The robot's task is to execute as many commands as possible without falling off the board. For example, on board 3 × 3, if the robot starts a sequence of actions s="RRDLUU" ("right", "right", "down", "left", "up", "up") from the central cell, the robot will perform one command, then the next command will force him to cross the edge. If the robot starts moving from the cell (2, 1) (second row, first column) then all commands will be executed successfully and the robot will stop at the cell (1, 2) (first row, second column).

<image> The robot starts from cell (2, 1) (second row, first column). It moves right, right, down, left, up, and up. In this case it ends in the cell (1, 2) (first row, second column).

Determine the cell from which the robot should start its movement in order to execute as many commands as possible.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The next 2t lines contain descriptions of the test cases.

In the description of each test case, the first line contains two integers n and m (1 ≤ n, m ≤ 10^6) — the height and width of the field that the robot is located on. The second line of the description is a string s consisting solely of characters 'L', 'R', 'D' and 'U' — the sequence of commands the robot executes. The string has a length from 1 to 10^6 commands.

It is guaranteed that the total length of s over all test cases does not exceed 10^6.

Output

Print t lines, each of which contains the answer to the corresponding test case. The answer to the test case are two integers r (1 ≤ r ≤ n) and c (1 ≤ c ≤ m), separated by a space — the coordinates of the cell (row number and column number) from which the robot should start moving to perform as many commands as possible.

If there are several such cells, you may output any of them.

Example

Input


4
1 1
L
1 2
L
3 3
RRDLUU
4 3
LUURRDDLLLUU


Output


1 1
1 2
2 1
3 2
import java.util.*;
import java.io.*;

public class E {

    public void prayGod() throws IOException {
        int t = nextInt();
        while (t-- > 0) {
            int n = nextInt();
            int m = nextInt();
            String s = next();

            int currX = 0, currY = 0;
            int lowX = 0, highX = 0;
            int lowY = 0, highY = 0;

            int finalX = 1, finalY = 1;

            for (int i = 0; i < s.length(); i++) {
                switch (s.charAt(i)) {
                case 'U': {
                    currX--;
                    break;
                }
                case 'L': {
                    currY--;
                    break;
                }
                case 'R': {
                    currY++;
                    break;
                }
                case 'D': {
                    currX++;
                    break;
                }
                default: {
                    System.exit(1);
                }
                }
                highX = Math.max(highX, currX);
                lowX = Math.min(lowX, currX);

                highY = Math.max(highY, currY);
                lowY = Math.min(lowY, currY);

                int boundX = highX - lowX + 1;
                int boundY = highY - lowY + 1;

                if (boundX <= n && boundY <= m) {
                    finalX = 1 - lowX;
                    finalY = 1 - lowY;
                } else {
                    break;
                }

            }
            out.printf("%d %d\n", finalX, finalY);

        }

    }

    public void printVerdict(boolean verdict) {
        if (verdict)
            out.println(VERDICT_YES);
        else
            out.println(VERDICT_NO);
    }

    static final String VERDICT_YES = "YES";
    static final String VERDICT_NO = "NO";
    static final boolean RUN_TIMING = true;
    static final boolean AUTOFLUSH = false;
    static final boolean FILE_INPUT = false;
    static final boolean FILE_OUTPUT = false;

    static int iinf = 0x3f3f3f3f;
    static long inf = (long) 1e18 + 10;
    static long mod = (long) 1e9 + 7;

    static char[] inputBuffer = new char[1 << 20];
    static PushbackReader in = new PushbackReader(new BufferedReader(new InputStreamReader(System.in)), 1 << 20);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), AUTOFLUSH);

    // int data-type
    public int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

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

    public void sort(int[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    public static void printArray(int[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    // long data-type
    public long nextLong() throws IOException {
        return Long.parseLong(next());
    }

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

    public static void printArray(long[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    public void sort(long[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    // double data-type
    public double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int n) throws IOException {
        double[] arr = new double[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextDouble();
        return arr;
    }

    public static void printArray(double[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    // Generic type
    public <T> void sort(T[] a) {
        shuffle(a);
        Arrays.sort(a);
    }

    public static <T> void printArray(T[] arr) {
        for (int i = 0; i < arr.length; i++)
            out.print(arr[i] + " ");
        out.println();
    }

    public String next() throws IOException {
        int len = 0;
        int c;
        do {
            c = in.read();
        } while (Character.isWhitespace(c) && c != -1);
        if (c == -1) {
            throw new NoSuchElementException("Reached EOF");
        }
        do {
            inputBuffer[len] = (char) c;
            len++;
            c = in.read();
        } while (!Character.isWhitespace(c) && c != -1);
        while (c != '\n' && Character.isWhitespace(c) && c != -1) {
            c = in.read();
        }
        if (c != -1 && c != '\n') {
            in.unread(c);
        }
        return new String(inputBuffer, 0, len);
    }

    public String nextLine() throws IOException {
        int len = 0;
        int c;
        while ((c = in.read()) != '\n' && c != -1) {
            if (c == '\r') {
                continue;
            }
            inputBuffer[len] = (char) c;
            len++;
        }
        return new String(inputBuffer, 0, len);
    }

    public boolean hasNext() throws IOException {
        String line = nextLine();
        if (line.isEmpty()) {
            return false;
        }
        in.unread('\n');
        in.unread(line.toCharArray());
        return true;
    }

    public void shuffle(int[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(long[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            long temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(Object[] arr) {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int) (Math.random() * (n - i));
            Object temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public static void main(String[] args) throws IOException {
        if (FILE_INPUT)
            in = new PushbackReader(new BufferedReader(new FileReader(new File("output.txt"))), 1 << 20);
        if (FILE_OUTPUT)
            out = new PrintWriter(new FileWriter(new File("output.txt")));

        long time = 0;
        time -= System.nanoTime();
        new E().prayGod();
        time += System.nanoTime();

        if (RUN_TIMING)
            System.err.printf("%.3f ms%n", time / 1000000.0);

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