Due to the coronavirus pandemic, city authorities obligated citizens to keep a social distance. The mayor of the city Semyon wants to light up Gluharniki park so that people could see each other even at night to keep the social distance.

The park is a rectangular table with n rows and m columns, where the cells of the table are squares, and the boundaries between the cells are streets. External borders are also streets. Every street has length 1. For example, park with n=m=2 has 12 streets.

You were assigned to develop a plan for lighting the park. You can put lanterns in the middle of the streets. The lamp lights two squares near it (or only one square if it stands on the border of the park).

<image> The park sizes are: n=4, m=5. The lighted squares are marked yellow. Please note that all streets have length 1. Lanterns are placed in the middle of the streets. In the picture not all the squares are lit.

Semyon wants to spend the least possible amount of money on lighting but also wants people throughout the park to keep a social distance. So he asks you to find the minimum number of lanterns that are required to light all the squares.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

Each test case is a line containing two integers n, m (1 ≤ n, m ≤ 10^4) — park sizes.

Output

Print t answers to the test cases. Each answer must be a single integer — the minimum number of lanterns that are required to light all the squares.

Example

Input


5
1 1
1 3
2 2
3 3
5 3


Output


1
2
2
5
8

Note

Possible optimal arrangement of the lanterns for the 2-nd test case of input data example: <image>

Possible optimal arrangement of the lanterns for the 3-rd test case of input data example: <image>
import java.util.*;
import java.io.*;
import java.util.stream.*;
public class Main{
	private static BufferedReader in;
	private static BufferedWriter out;
	
	public static void main(String[] args) throws IOException {
		open();

		StringTokenizer st;
		StringBuilder sb;
	
		int t=readInt();
		while(t-->0) {
			st=new StringTokenizer(readString());
			int n=Integer.parseInt(st.nextToken());
			int m=Integer.parseInt(st.nextToken());
			int ans=0;
			if(n==1&&m==1)
				out.write("1\n");
			else{
				ans=((n*m)/2);
				if(n*m%2!=0)
					ans++;
				out.write(ans+"\n");
			}
		}
		
		close();
	}
	static class Pair<X,Y>{
		X first;
		Y second;
	}
	public static int gcd(int a,int b) {
		if(a==0)
			return b;
		return gcd(b%a,a);
	}
	static int count(int x, int[] arr) {
		int count = 0;
 
		for (int i = 0; i < arr.length; i++)
			if (arr[i] == x)
				count++;
		return count;
	}
 
	public static String reverseString(String str) {
		StringBuilder sb = new StringBuilder(str);
		sb.reverse();
		return sb.toString();
	}
 
	static boolean isPalindrome(String str) {
		int i = 0, j = str.length() - 1;
 
		while (i < j) {
 
			if (str.charAt(i) != str.charAt(j))
				return false;
 
			i++;
			j--;
		}
		return true;
	}
	static int modInverse(int a, int m) {
		int g = gcd(a, m);
		if (g != 1)
			return -1;
		else
			return power(a, m - 2, m);
 
	}
 
	// To compute x^y under modulo m
	static int power(int x, int y, int m) {
		if (y == 0)
			return 1;
 
		int p = power(x, y / 2, m) % m;
		p = (p * p) % m;
 
		if (y % 2 == 0)
			return p;
		else
			return (x * p) % m;
	}
 
	static int[] primeGenerator(int num) {
		int length = 0, arr[] = new int[num], a = num, factor = 1;
		if (num % 2 == 0) {
			while (num % 2 == 0) {
				num /= 2;
				factor *= 2;
			}
			arr[length++] = factor;
		}
		for (int i = 3; i * i <= a; i++) {
			factor = 1;
			if (num % i == 0) {
				while (num % i == 0) {
					num /= i;
					factor *= i;
				}
				arr[length++] = factor;
			}
		}
		if (num > 1)
			arr[length++] = num;
		return Arrays.copyOfRange(arr, 0, length);
	}
 
	static boolean isPrime(int n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
 
		// This is checked so that we can skip
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;
 
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
 
		return true;
	}
	private static int[] readInts() throws IOException {
		return Stream.of(in.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
	}
	private static int readInt() throws IOException {
		return Integer.parseInt(in.readLine());
	}
	private static long[] readLongs() throws IOException {
		return Stream.of(in.readLine().split(" ")).mapToLong(Long::parseLong).toArray();
	}
	private static long readLong() throws IOException {
		return Long.parseLong(in.readLine());
	}
	private static double[] readDoubles() throws IOException {
		return Stream.of(in.readLine().split(" ")).mapToDouble(Double::parseDouble).toArray();
	}
	private static double readDouble() throws IOException {
		return Double.parseDouble(in.readLine());
	}
	private static String readString() throws IOException {
		return in.readLine();
	}
	private static int modulo(int S, int N) {
		return ((S) & (N - 1));
	} // returns S % N, where N is a power of 2
	private static boolean isPowerOfTwo(int S) {
		return (S & (S - 1)) == 0 ? true : false;
	}
	private static void open() {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new BufferedWriter(new OutputStreamWriter((System.out)));
	}
	private static void close() throws IOException {
		out.flush();
		out.close();
		in.close();
	}
	
}