Problem: This is a harder version of the problem. The difference is only in constraints.

You are given a rectangular n × m matrix a. In one move you can choose any column and cyclically shift elements in this column. You can perform this operation as many times as you want (possibly zero). You can perform this operation to a column multiple times.

After you are done with cyclical shifts, you compute for every row the maximal value in it. Suppose that for i-th row it is equal r_i. What is the maximal possible value of r_1+r_2+…+r_n?

Input

The first line contains an integer t (1 ≤ t ≤ 40), the number of test cases in the input.

The first line of each test case contains integers n and m (1 ≤ n ≤ 12, 1 ≤ m ≤ 2000) — the number of rows and the number of columns in the given matrix a. 

Each of the following n lines contains m integers, the elements of a (1 ≤ a_{i, j} ≤ 10^5).

Output

Print t integers: answers for all test cases in the order they are given in the input.

Example

Input


3
2 3
2 5 7
4 2 4
3 6
4 1 5 2 10 4
8 6 6 4 9 10
5 4 9 5 8 7
3 3
9 9 9
1 1 1
1 1 1


Output


12
29
27

Note

In the first test case you can shift the third column down by one, this way there will be r_1 = 5 and r_2 = 7.

In the second case you can don't rotate anything at all, this way there will be r_1 = r_2 = 10 and r_3 = 9.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class Main{
	static int[][]memo;
	static int n,m,in[][];
	static int dp(int col,int maxRowMask) {
		if(col>=Math.min(n, m) || maxRowMask==((1<<n)-1))return 0;
		if(memo[col][maxRowMask]!=-1)return memo[col][maxRowMask];
		
		int ans=0;
		
		int availableBits=maxRowMask^((1<<n)-1);
		//all masks that don't intersect with maxRowMask
		for(int colMask=availableBits;colMask!=0;colMask=(colMask-1)&availableBits) {
			
			ans=Math.max(ans, maxMask[col][colMask]+dp(col+1, maxRowMask|colMask));
			
		}
		return memo[col][maxRowMask]=ans;
	}
	static int[][]sumOfMask;
	static int[][]maxMask;
	public static void main(String[] args) throws Exception{
		pw=new PrintWriter(System.out);
		sc = new MScanner(System.in);
		int tc=sc.nextInt();
		while(tc-->0) {
			n=sc.nextInt();m=sc.nextInt();
			
			int[]maxInCol=new int[m];
			in=new int[m][n+1];
			
			for(int i=0;i<n;i++) {
				for(int j=0;j<m;j++) {
					in[j][i]=sc.nextInt();
					maxInCol[j]=Math.max(maxInCol[j], in[j][i]);
					in[j][n]=j;
				}
			}
			Arrays.sort(in,(x,y)->maxInCol[y[n]]-maxInCol[x[n]]);
			
			
			memo=new int[n][1<<n];
			sumOfMask=new int[n][1<<n];
			maxMask=new int[n][1<<n];
			for(int i=0;i<n;i++) {
				for(int msk=0;msk<memo[i].length;msk++) {
					memo[i][msk]=-1;
					if(i>=m)continue;
					for(int bit=0;bit<n;bit++) {
						if(((msk>>bit)&1)!=0) {
							sumOfMask[i][msk]+=in[i][bit];
						}
					}
				}
			}
			for(int col=0;col<n;col++) {
				for(int msk=0;msk<(1<<n);msk++) {
					int curMask=msk;
					for(int cyclicShift=0;cyclicShift<n;cyclicShift++) {
						maxMask[col][msk]=Math.max(maxMask[col][msk], sumOfMask[col][curMask]);
						
						int lastBit=curMask&1;
						curMask>>=1;
						curMask|=(lastBit<<(n-1));
						
					}
				}
			}
			pw.println(dp(0, 0));
		}
		
		
		pw.flush();
	}
	static PrintWriter pw;
	static MScanner  sc;
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void shuffle(int[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			int tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static void shuffle(long[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			long tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
}