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>
	                       //ARNAV KUMAR MANDAL//
                                     //XYPHER//
 
 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;
import java.io.*;
 
public class Solution{
//--------------------------MAIN---------------------------------------------------------------------//
	public static void main(String[] args) throws IOException {
		int tc = ni();
		while(tc-->0) {
			long n = ni();
			long m = ni();
			if(n%2==0 || m%2==0)opl((n*m)/2);
			else {
				long y = Math.max(m,n);
				long x = Math.min(m,n);
				long z = x*(y-1)/2;
				z += x/2 + 1;
				opl(z);
			}
			
			
		}
	}
	
	
//--------------------------FAST IO objects/methods--------------------------------------------------//
	
	static Reader in= new Reader(System.in);
	static OutputWriter out = new OutputWriter(System.out);
	private static int ni(){int n = in.nextInt();return n;}
	private static long nl(){long n = in.nextLong();return n;}
	private double nd(){return Double.parseDouble(ns()); }
	private static String ns(){String s = in.nextString();return s;}
	private static int[] nai(int n){int[] a = new int[n];for(int i = 0;i < n;i++)a[i] = ni();return a;}
	private static long[] nal(int n){long[] a = new long[n];for(int i = 0;i < n;i++)a[i] = nl();return a;}
	private static StringBuilder sb(String s){StringBuilder S = new StringBuilder(s);return S;}
	private static HashSet<Integer> hsi(){HashSet<Integer> s = new HashSet<Integer>();return s;}
	private static HashSet<Long> hsl(){HashSet<Long> s = new HashSet<Long>();return s;}
	private static HashMap<Integer,Integer> hmii(){HashMap<Integer,Integer> h = new HashMap<Integer,Integer>();return h;}
	private static HashMap<Long,Long> hmll(){HashMap<Long,Long> h = new HashMap<Long,Long>();return h;}
	private static HashMap<String,Integer> hmsi(){HashMap<String,Integer> h = new HashMap<String,Integer>();return h;}
	private static int[][] nmi(int n, int m){int A[][] = new int[n][m];for(int i=0;i<n;i++){for(int j=0;j<m;j++) {A[i][j] = ni();}}return A;}
	private static char[][] nmc(int n, int m){char A[][] = new char[n][m];for(int i=0;i<n;i++){StringBuilder s=sb(ns());for(int j=0;j<m;j++){A[i][j]=s.charAt(j);}}return A;}
	private static void op(Object o) {out.print(o);}
	private static void opl(Object o) {out.println(o);}
	private static void opai(int[] o){for(int a:o)op(a+" ");opl("");}
	private static void opad(double[] o){for(double a:o)op(a+" ");opl("");}
	private static void opal(long[] o){for(long a:o)op(a+" ");opl("");}
	private static void opac(char[] o){for(char a:o)op(a);opl("");}
	private static void opas(String[] o){for(String a:o)op(a+" ");opl("");}
	private static void opmi(int[][] o) {for(int i=0;i<o.length;i++)opai(o[i]);}
	private static void opml(long[][] o) {for(int i=0;i<o.length;i++)opal(o[i]);}
	private static void opmc(char[][] o) {for(int i=0;i<o.length;i++)opac(o[i]);}

//--------------------------FAST IO------------------------------------------------------------------//
	private static class Reader {
		private InputStream stream;
		private byte[] buf = new byte[4*1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public Reader(InputStream stream) {
			this.stream = stream;
		}
		
		public int read() {
			if (numChars == -1) {
				throw new InputMismatchException();
			}
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}
		
		public int nextInt() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		
		public String nextString() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
		
		public double nextDouble() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c == 'e' || c == 'E') {
					return res * Math.pow(10, nextInt());
				}
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c == 'e' || c == 'E') {
						return res * Math.pow(10, nextInt());
					}
					if (c < '0' || c > '9') {
						throw new InputMismatchException();
					}
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public long nextLong() {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9') {
					throw new InputMismatchException();
				}
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
		
		public boolean isSpaceChar(int c) {
			if (filter != null) {
				return filter.isSpaceChar(c);
			}
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		
		public String next() {
			return nextString();
		}
		
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	private static class OutputWriter {
		private final PrintWriter writer;
		
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
		
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
		
		
		
		public void println(Object... objects) {
			print(objects);
			writer.println();
			writer.flush();
		}
		
		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0) {
					writer.print(' ');
				}
				writer.print(objects[i]);
			}
			writer.flush();
		}
		
		public void close() {
			writer.close();
		}
		
		public void flush() {
			writer.flush();
		}
	}
}  