The country of Siruseri has A∗B$A*B$ districts. You want to create A$A$ states from these districts, such that each state has exactly B$B$ districts, and each district is part of exactly one state. You don't care about the geographical location of the districts. You can pick any B$B$ districts and make it into a state.
There are only two parties contesting in the coming elections: P1$P_1$ and P2$P_2$. You know the number of votes that each party receives in each district. In the i-th district, P1$P_1$ gets ci$c_i$ votes and P2$P_2$ gets di$d_i$ votes. You are guaranteed that all these 2∗A∗B$2*A*B$ integers (the number of votes received by each party in the districts) are distinct. Also, both A$A$ and B$B$ are odd. 
Suppose you have chosen which districts belong to which states, then, to find out who wins any particular state, they follow a weird rule: Suppose the number of votes that P1$P_1$ gets in the B$B$ districts of a particular state are x1,x2,…,xB$x_1, x_2, \ldots, x_B$, and the number of votes that P2$P_2$ gets in the B$B$ districts of this state are y1,y2,…,yB$y_1, y_2, \ldots, y_B$. Then among all these 2∗B$2*B$ numbers, the largest number is chosen (note that we are guaranteed of an unique largest number). If that number is some xi$x_i$, then P1$P_1$ wins this state. If the largest number is some yj$y_j$, then P2$P_2$ wins this state.
You secretly support the party P1$P_1$, and hence you want to assign the districts to states, in such a way, that the number of states won by P1$P_1$ is maximized. Find this maximum number of states that P1$P_1$ can win.
Note that ci$c_i$ and di$d_i$ will always remain associated with the i-th district. If the i-th district gets assigned to a particular state, then both ci$c_i$ and di$d_i$ will be considered when deciding who won that state.

-----Input:-----
- The first line of the input contains a single integer, T$T$, the number of testcases. The description of each testcase follows.
- The first line of each testcase contains two integers, A$A$ and B$B$.
- The second line of each testcase contains A∗B$A*B$ integers: c1,c2,…,cA∗B$c_1, c_2, \ldots, c_{A*B}$, the number of votes won by P1$P_1$ in the districts.
- The third line of each testcase contains A∗B$A*B$ integers: d1,d2,…,dA∗B$d_1, d_2, \ldots, d_{A*B}$, the number of votes won by P2$P_2$ in the districts.

-----Output:-----
For each testcase output a single line which contains the maximum number of states that P1$P_1$ can win.

-----Constraints:-----
- 1≤T≤5$1 \leq T \leq 5$
- 1≤A,B$1 \leq A, B$
- A∗B≤105$A*B \leq 10^5$
- A$A$, B$B$ are odd
- 1≤ci,di≤109$1 \leq c_i, d_i \leq 10^9$
- All the ci$c_i$ and di$d_i$ will be distinct.

-----Sample Input:-----
3
1 3
4 2 9
5 6 7
1 3
4 2 9
5 10 7
3 3
7 14 11 4 15 5 20 1 17
2 13 16 9 19 6 12 8 10

-----Sample Output:-----
1
0
3

-----Explanation:-----
Testcase 1: Since you have to form only 1 state, there is no choice, but to put all the 3 districts in that same state. Now to figure out who wins that single state, we take the maximum among {4, 2, 9, 5, 6, 7}. The maximum is 9, and that belongs to P1$P_1$. Hence P1$P_1$ wins this state. And because they have won 1 state, the answer is 1.
Testcase 2: Similarly, there is no choice here. To figure out who wins that single state, we take the maximum among {4, 2, 9, 5, 10, 7}. The maximum is 10, and that belongs to P2$P_2$. Hence P2$P_2$ wins this state. And because P1$P_1$ have won no states, the answer is 0.
Testcase 3: We need to make three states with three districts each. Suppose we that the 3rd, 5th and 7th districts and form a state, the votes in them would be {11, 16, 15, 19, 20, 12}. The max among these is 20, and that belongs to P1$P_1$. Hence P1$P_1$ would win this state. 
Similarly, suppose we make the second state with the 2nd, 4th and 8th districts, the votes in them would be {14, 13, 4, 9, 1, 8}. The max among these is 14, and that belongs to P1$P_1$. Hence P1$P_1$ would win this state. 
The remaining three districts: 1st, 6th and 9th districts form the third state. The votes in them would be {7, 2, 5, 6, 17, 10}. The max among these is 17, and that belongs to P1$P_1$. Hence P1$P_1$ would win this state. 
In this situation, P1$P_1$ wins three states. You obviously cannot do any better. Hence the answer is 3.

Difficulty: interview

Starter code:

Solutions:
# cook your dish here
for _ in range(int(input())):
    A,B=list(map(int,input().split()))
    l1=list(map(int,input().split()))
    l2=list(map(int,input().split()))
    for i in range(A*B):
     if l1[i]<l2[i]:
      l1[i]=0
     else:
      l2[i]=0
    l1.sort(reverse=True)
    l2.sort(reverse=True)
 
    w,d,c=0,0,0
    for j in range(A):
     if l1[c]>l2[d]:
      w+=1
      c+=1
      d+=B-1
     else:
      d+=B
    print(w)
   


# cook your dish here
# cook your dish here
for i in range(int(input())):
    a,b=[int(i) for i in input().split()]
    l1=[int(i) for i in input().split()]
    l2=[int(i) for i in input().split()]
    l=[]
    for i in range(a*b):
     if(l1[i]>l2[i]):
      l.append([l1[i],1])
     else:
      l.append([l2[i],2])
    l.sort()
    arr=[]
    for i in range(a*b):
     if(l[i][1]==1):
      arr.append(i+1)
    j=1
    ans=0
    for i in range(len(arr)):
     if(arr[i]>=j*b):
      ans+=1 
      j+=1 
    print(ans)
  


# cook your dish here
for i in range(int(input())):
    a,b=[int(i) for i in input().split()]
    l1=[int(i) for i in input().split()]
    l2=[int(i) for i in input().split()]
    l=[]
    for i in range(a*b):
     if(l1[i]>l2[i]):
      l.append([l1[i],1])
     else:
      l.append([l2[i],2])
    l.sort()
    arr=[]
    for i in range(a*b):
     if(l[i][1]==1):
      arr.append(i+1)
    j=1
    ans=0
    for i in range(len(arr)):
     if(arr[i]>=j*b):
      ans+=1 
      j+=1 
    print(ans)
  
 


T=int(input())
for _ in range(T):
    A,B=list(map(int,input().split()))
    cs=list(map(int,input().split()))
    ds=list(map(int,input().split()))
 
    for i in range(A*B):
     if cs[i]<ds[i]:
      cs[i]=0
     else:
      ds[i]=0

    cs.sort(reverse=True)
    ds.sort(reverse=True)

    w,c,d=0,0,0
    for _ in range(A):
     if cs[c]>ds[d]:
      w+=1
      c+=1
      d+=B-1
     else:
      d+=B
   
    print(w)


# Enter your code here. Read input from STDIN. Print output to STDOUT
t = int(input())
for i in range(int(t)):
    A ,B = list(map(int,input().split()))
    C = list(map(int,input().split()))
    D = list(map(int,input().split()))
    for j in range(A*B):
     if C[j]>D[j]:
      D[j] = 0
     else:
      C[j] = 0
    C.sort(reverse=True)
    D.sort(reverse=True)
    v = 0
    j = 0
    k = 0
    for _ in range(A):
     if C[j] > D[k]:
      v+=1
      j+=1
      k+=B-1
     else:
      k+=B
    print(v)