You are given two integers x and y. You can perform two types of operations: 

  1. Pay a dollars and increase or decrease any of these integers by 1. For example, if x = 0 and y = 7 there are four possible outcomes after this operation: 
    * x = 0, y = 6; 
    * x = 0, y = 8; 
    * x = -1, y = 7; 
    * x = 1, y = 7. 

  2. Pay b dollars and increase or decrease both integers by 1. For example, if x = 0 and y = 7 there are two possible outcomes after this operation: 
    * x = -1, y = 6; 
    * x = 1, y = 8. 



Your goal is to make both given integers equal zero simultaneously, i.e. x = y = 0. There are no other requirements. In particular, it is possible to move from x=1, y=0 to x=y=0.

Calculate the minimum amount of dollars you have to spend on it.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of testcases.

The first line of each test case contains two integers x and y (0 ≤ x, y ≤ 10^9).

The second line of each test case contains two integers a and b (1 ≤ a, b ≤ 10^9).

Output

For each test case print one integer — the minimum amount of dollars you have to spend.

Example

Input


2
1 3
391 555
0 0
9 4


Output


1337
0

Note

In the first test case you can perform the following sequence of operations: first, second, first. This way you spend 391 + 555 + 391 = 1337 dollars.

In the second test case both integers are equal to zero initially, so you dont' have to spend money.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;
import java.util.function.*;
import java.util.stream.*;


public class A {

    private static final FastReader in = new FastReader();
    private static final FastWriter out = new FastWriter();

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

    private void run() {
        var t = in.nextInt();
        while (t-- > 0) {
            solve();
        }

        out.flush();
    }

    private void solve() {
        var x = in.nextLong();
        var y = in.nextLong();
        var a = in.nextLong();
        var b = in.nextLong();

        var ans = Math.abs(x - y) * a + Math.min(x, y) * b;
        ans = Math.min(ans, (x + y) * a);

        out.println(ans);
    }

}


class FastReader {

    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static StringTokenizer in;

    public String next() {
        while (in == null || !in.hasMoreTokens()) {
            try {
                in = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                return null;
            }
        }
        return in.nextToken();
    }

    public BigDecimal nextBigDecimal() {
        return new BigDecimal(next());
    }

    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }

    public boolean nextBoolean() {
        return Boolean.valueOf(next());
    }

    public byte nextByte() {
        return Byte.valueOf(next());
    }

    public double nextDouble() {
        return Double.valueOf(next());
    }

    public double[] nextDoubleArray(int length) {
        var a = new double[length];
        for (var i = 0; i < length; i++) {
            a[i] = nextDouble();
        }
        return a;
    }

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

    public int[] nextIntArray(int length) {
        var a = new int[length];
        for (var i = 0; i < length; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public long nextLong() {
        return Long.valueOf(next());
    }

    public long[] nextLongArray(int length) {
        var a = new long[length];
        for (var i = 0; i < length; i++) {
            a[i] = nextLong();
        }
        return a;
    }

}


class FastWriter extends PrintWriter {

    public FastWriter() {
        super(System.out);
    }

    public void println(boolean[] a) {
        for (var i = 0; i < a.length; i++) {
            print(a[i]);
            print(i + 1 < a.length ? ' ' : '\n');
        }
    }

    public void println(double[] a) {
        for (var i = 0; i < a.length; i++) {
            print(a[i]);
            print(i + 1 < a.length ? ' ' : '\n');
        }
    }

    public void println(int[] a) {
        for (var i = 0; i < a.length; i++) {
            print(a[i]);
            print(i + 1 < a.length ? ' ' : '\n');
        }
    }

    public void println(long[] a) {
        for (var i = 0; i < a.length; i++) {
            print(a[i]);
            print(i + 1 < a.length ? ' ' : '\n');
        }
    }

    public void println(Object... a) {
        for (var i = 0; i < a.length; i++) {
            print(a[i]);
            print(i + 1 < a.length ? ' ' : '\n');
        }
    }

    public <T> void println(List<T> l) {
        println(l.toArray());
    }

    public void debug(String name, Object o) {
        String value = Arrays.deepToString(new Object[] { o });
        value = value.substring(1, value.length() - 1);
        System.err.println(name + " => " + value);
    }

}
