You are given a string s consisting of lowercase English letters and a number k. Let's call a string consisting of lowercase English letters beautiful if the number of occurrences of each letter in that string is divisible by k. You are asked to find the lexicographically smallest beautiful string of length n, which is lexicographically greater or equal to string s. If such a string does not exist, output -1.

A string a is lexicographically smaller than a string b if and only if one of the following holds: 

  * a is a prefix of b, but a ≠ b; 
  * in the first position where a and b differ, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b. 

Input

The first line contains a single integer T (1 ≤ T ≤ 10 000) — the number of test cases.

The next 2 ⋅ T lines contain the description of test cases. The description of each test case consists of two lines.

The first line of the description contains two integers n and k (1 ≤ k ≤ n ≤ 10^5) — the length of string s and number k respectively.

The second line contains string s consisting of lowercase English letters.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case output in a separate line lexicographically smallest beautiful string of length n, which is greater or equal to string s, or -1 if such a string does not exist.

Example

Input


4
4 2
abcd
3 1
abc
4 3
aaaa
9 3
abaabaaaa


Output


acac
abc
-1
abaabaaab

Note

In the first test case "acac" is greater than or equal to s, and each letter appears 2 or 0 times in it, so it is beautiful.

In the second test case each letter appears 0 or 1 times in s, so s itself is the answer.

We can show that there is no suitable string in the third test case.

In the fourth test case each letter appears 0, 3, or 6 times in "abaabaaab". All these integers are divisible by 3.
#!/usr/bin/env python
from __future__ import division, print_function
import math
import os
import sys
from sys import stdin,stdout
from io import BytesIO, IOBase
from collections import deque
#sys.setrecursionlimit(10**5)
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip


# region fastio

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")
#-----------------------------------------------------------------
def binarySearchCount(arr, n, key):
    left = 0
    right = n - 1

    count = 0

    while (left <= right):
        mid = int((right + left) / 2)

        # Check if middle element is
        # less than or equal to key
        if (arr[mid] < key):
            count = mid + 1
            left = mid + 1

        # If key is smaller, ignore right half
        else:
            right = mid - 1
    return count
def regularbracket(t):
    p=0
    for i in t:
        if i=="(":
            p+=1
        else:
            p-=1
        if p<0:
            return False
    else:
        if p>0:
            return False
        else:
            return True
# endregion
"""
def samesign(a,b):
    if (a>0 and b>0) or (a<0 and b<0):
        return True
    return False
def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        arr = list(map(int,input().split()))
        sum1=0
        l=[arr[0]]
        for i in range(len(arr)-1):
            if samesign(arr[i+1],arr[i])==True:
                l.append(arr[i+1])
            else:
              #  print(l)
               # print(max(l))
                sum1+=max(l)
                l=[arr[i+1]]
        #print(sum1)
       # print(l)
        sum1+=max(l)
        print(sum1)
"""
"""
def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        arr = list(map(int,input().split()))
        sum1 = sum(arr)
     #   max1 = max(arr)
        arr = sorted(arr)
        flag = True
        for i in range(1,n+1):
            if arr[i-1]>i:
                print("second")
                flag = False
                break
        if flag==True:
            diff = (n*(n+1))/2-sum1
            if diff%2==0:
                print("Second")
            else:
                print("First")
"""
"""
def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        a = list(map(int,input().split()))
        seg = [0] * (n + 1)
        curr = 0
        cnt = 0
        for ai in a:
            if ai == curr:
                cnt += 1
            else:
                if cnt > 0:
                    seg[curr] += 1
                curr = ai
                cnt = 1
        if cnt > 0:
            seg[curr] += 1
        res = n
        for i in range(1, n + 1):
            if seg[i] == 0:
                continue
            op = seg[i] + 1
            if i == a[0]:
                op -= 1
            if i == a[-1]:
                op -= 1
            res = min(res, op)
        print((res))
"""
"""
def main():
    t = int(input())
    for _ in range(t):
        a,b = map(int,input().split())
        if a==0 or b==0:
            print(0)
        elif a>=2*b or b>=2*a:
            print(min(a,b))
        else:
            print((a+b)//3)
"""
"""
def main():
    t = int(input())
    for _ in range(t):
        n, m, x, y = map(int, input().split())
        ans = 0
        y = min(y, 2 * x)
        for i_ in range(n):
            s = input()
            i = 0
            while i < m:
                if s[i] == '*':
                    i += 1
                    continue
                j = i
                while j + 1 < m and s[j + 1] == '.':
                    j += 1
                l = j - i + 1
                ans += l % 2 * x + l // 2 * y
                i = j + 1
        print(ans)
"""
"""
def main():
    t = int(input())
    for _ in range(t):
        n,x = map(int,input().split())
        arr = list(map(int,input().split()))
        p=0
        sum1 = sum(arr)
        arr = sorted(arr)
        if sum1//n>=x:
            print(n)
        else:
            for i in range(n-1):
                sum1-=arr[i]
                if sum1//(n-(i+1))>=x:
                    print(n-(i+1))
                    break
            else:
                print(0)
"""
"""
def main():
    p = int(input())
    for _ in range(p):
        n,k = map(int,input().split())
        list1=[]
        if n==1 and k==1:
            print(0)
        else:
            for i in range(n,0,-1):
                if i+(i-1)<=k:
                    list1.append(i)
                    break
                else:
                    list1.append(i)
            list1.remove(k)
            print(len(list1))
            print(*list1)
"""
"""
def mirrortime(s):
    s = list(s)
    pp=""
    for i in range(len(s)):
        if s[i]=="0":
            continue
        elif s[i]=="2":
            s[i]="5"
        elif s[i]=="5":
            s[i]="2"
        elif i=="8":
            continue
        elif i=="1":
            continue
    for i in s:
        pp+=i
    return pp
#print(mirrortime("2255"))
def main():
    t = int(input())
    for _ in range(t):
        l=[3,4,6,7,9]
        h,m = map(int,input().split())
        s = input()
        t=s[0:2]
        p=s[3:5]
        ll=[]
        mm=[]
        t = int(t)
        p = int(p)
     #   print(t,p)
        for i in range(t,h):
            for j in range(p,m):
                i = str(i)
                if len(i)==1:
                    i="0"+i
                j = str(j)
                if len(j)==1:
                    j="0"+j
                if int(i[0]) in l or int(i[1]) in l or int(j[0]) in l or int(j[1]) in l:
                    continue
                else:
                    ll.append(i)
                    mm.append(j)
            p=0
     #   print(ll,mm)
        if len(ll)>=1:
            for i in range(len(ll)):
                cccc = ll[i]
                dddd = mm[i]
                ccc = mirrortime(cccc)
                ddd = mirrortime(dddd)
                ccc = list(ccc)
                ddd = list(ddd)
                ccc.reverse()
                ddd.reverse()
                ppp=""
                qqq=""
                for k in ccc:
                    ppp+=k
                for k_ in ddd:
                    qqq+=k_
                if int(qqq)<h and int(ppp)<m:
                   # print(int(qqq))
                   # print(int(ppp))
                    print(cccc+":"+dddd)
                    break
            else:
                print("00:00")

        else:
            print("00:00")
"""
"""
def main():
    n,x = map(int,input().split())
    cnt=0
    for _ in range(n):
        yn,ice = map(str,input().split())
        if yn=="+":
            x+=int(ice)
        else:
            x-=int(ice)
            if x<0:
                cnt+=1
                x+=int(ice)
    print(max(0,x),cnt)
"""
"""
def main():
    t = int(input())
    for _ in range(t):
        cnt=0
        l=[]
        s = input()
        if "1" not in s:
            print(0)
        else:
            cnt=0
            for i in s:
                if i=="0":
                    cnt+=1
                if i=="1":
                    l.append(cnt)
                    cnt=0
            if s[len(s)-1]!=1:
                l.append(cnt)
           # print(l)
            if s[0]=="0":
                l.remove(l[0])
            if s[len(s)-1]=="0":
                l.remove(l[len(l)-1])
            print(sum(l))
"""
def main():
    d={}
    for i in range(26):
        d[chr(i+97)]=i
    for _ in range(int(input())):
        n, k = [int(s) for s in input().split()]
        s = input().strip()
        if n % k != 0:
            print(-1)
            continue
        pre = [[0 for i in range(26)] for j in range(n + 1)]
        for i in range(n):
            for j in range(26):
                pre[i][j] = pre[i - 1][j]
            pre[i][d[s[i]]] += 1
        for j in range(26):
            if pre[n - 1][j] % k != 0:
                break
        else:
            print(s)
            continue
        for i in range(n - 1, -1, -1):
            req = {}
            sumr = 0
            for j in range(26):
                if pre[i - 1][j] % k != 0:
                    req[chr(j + ord('a'))] = k - (pre[i - 1][j] % k)
                    sumr += (k - (pre[i - 1][j] % k))
            if sumr <= n - i and s[i] != 'z':
                if (n - i - sumr) % k == 0:
                    ans = s[:i]
                    flag = 0
                    if n - i - sumr > 0:
                        if chr(ord(s[i]) + 1) in req:
                            req[chr(ord(s[i]) + 1)] -= 1
                        else:
                            req[chr(ord(s[i]) + 1)] = k - 1
                            sumr += k
                        ans += chr(ord(s[i]) + 1)
                        flag = 1
                    req1 = sorted([[c, req[c]] for c in req])
                    if not flag:
                        for w in range(len(req1)):
                            if req1[w][0] > s[i]:
                                ans += req1[w][0]
                                req1[w][1] -= 1
                                flag = 1
                                break
                    if not flag:
                        continue
                    ans += "a" * (n - i - sumr)
                    for w in range(len(req1)):
                        ans += req1[w][0] * req1[w][1]
                    print(ans)
                    break
        else:
            print(-1)
if __name__ == '__main__':
    main()