human
Can you provide a Python program to determine if it is possible to convert string a into b after performing some (possibly zero) operations on it given the following:
Ashish has two strings a and b, each of length n, and an integer k. The strings only contain lowercase English letters.

He wants to convert string a into string b by performing some (possibly zero) operations on a.

In one move, he can either 

  * choose an index i (1 ≤ i≤ n-1) and swap a_i and a_{i+1}, or 
  * choose an index i (1 ≤ i ≤ n-k+1) and if a_i, a_{i+1}, …, a_{i+k-1} are all equal to some character c (c ≠ 'z'), replace each one with the next character (c+1), that is, 'a' is replaced by 'b', 'b' is replaced by 'c' and so on. 


Note that he can perform any number of operations, and the operations can only be performed on string a. 

Help Ashish determine if it is possible to convert string a into b after performing some (possibly zero) operations on it.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of each test case is as follows.

The first line of each test case contains two integers n (2 ≤ n ≤ 10^6) and k (1 ≤ k ≤ n).

The second line of each test case contains the string a of length n consisting of lowercase English letters.

The third line of each test case contains the string b of length n consisting of lowercase English letters.

It is guaranteed that the sum of values n among all test cases does not exceed 10^6.

Output

For each test case, print "Yes" if Ashish can convert a into b after some moves, else print "No".

You may print the letters of the answer in any case (upper or lower).

Example

Input

4
3 3
abc
bcd
4 2
abba
azza
2 1
zz
aa
6 2
aaabba
ddddcc

Output

No
Yes
No
Yes

Note

In the first test case it can be shown that it is impossible to convert a into b.

In the second test case,

"abba" \xrightarrow{inc} "acca" \xrightarrow{inc} … \xrightarrow{inc} "azza".

Here "swap" denotes an operation of the first type, and "inc" denotes an operation of the second type.

In the fourth test case,

"aaabba" \xrightarrow{swap} "aaabab" \xrightarrow{swap} "aaaabb" \xrightarrow{inc} … \xrightarrow{inc} "ddaabb"...
Solve the task in PYTHON3.
assistant
#Here is Python program to determine if it is possible to convert string a into b after performing some (possibly zero) operations on it.

import sys, os
import heapq, functools, collections
import math, random
from collections import Counter, defaultdict

# available on Google, not available on Codeforces
# import numpy as np
# import scipy

def solve_(arr,brr,k):
    # your solution here

    x = Counter(arr)
    y = Counter(brr)

    for bef,aft in zip("abcdefghijklmnopqrstuvwxy", "bcdefghijklmnopqrstuvwxyz"):
        if y[bef] > x[bef]:
            return "No"
        deductible = x[bef] - y[bef]
        if deductible == 0:
            continue
        if deductible%k != 0:
            return "No"
        x[bef] -= deductible
        x[aft] += deductible

    return "Yes"

def console(*args):  
    # print on terminal in different color
    print('\033[36m', *args, '\033[0m', file=sys.stderr)
    pass

ONLINE_JUDGE = False

# if Codeforces environment
if os.path.exists('input.txt'):
    ONLINE_JUDGE = True

if ONLINE_JUDGE:
    sys.stdin = open("input.txt","r")
    sys.stdout = open("output.txt","w")

    def console(*args):
        pass

def solve(*args):
    # screen input
    # if not ONLINE_JUDGE:
    #     console("----- solving ------")
    #     console(*args)
    #     console("----- ------- ------")
    return solve_(*args)

if True:
    # if memory is not a constraint
    inp = iter(sys.stdin.readlines())
    input = lambda: next(inp)
else:
    # if memory is a constraint
    input = sys.stdin.readline

for case_num in range(int(input())):

    _,k = list(map(int,input().split()))
    # read line as a string
    arr = input().strip()
    brr = input().strip()

    # read line as an integer
    # k = int(input())
    
    # read one line and parse each word as a string
    # lst = input().split()

    # read one line and parse each word as an integer

    # read matrix and parse as integers (after reading read nrows)
    # lst = list(map(int,input().split()))
    # nrows = lst[0]  # index containing information, please change
    # grid = []
    # for _ in range(nrows):
    #     grid.append(list(map(int,input().split())))

  ...