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.
import java.io.*;
import java.util.*;
import java.lang.*;
public class Main2{
    static InputReader sc;
    static PrintWriter pw;
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        sc = new InputReader(inputStream);
        pw = new PrintWriter(outputStream);
        solve();
        pw.close();
    }
    // static int L,R,top,bottom;
    // static int cnt,edge;
    public static void solve() {
        int t=sc.nextInt();
        // int t=1;
        u:while(t-->0){
            int n=s(0);
            int k=s(0);
            String s=s("");
            if(n%k!=0){
                pln(-1);
                continue;
            }                
            int []arr=new int[26];
            for(char c:s.toCharArray())
                arr[c-'a']++;
            boolean isIt=true;
            for(int i=0;i<26;i++){
                if(arr[i]%k!=0){
                    isIt=false;
                    break;                    
                }
            }
            if(isIt){
                pln(s);
                continue u;
            }            
            int []prefix=new int [26];  
            int sum=0,temp;          
            int p=0,idx=0;
            char chrr='a';
            for(char c:s.toCharArray()){
                for(int i=(c-'a')+1;i<26;i++){                         
                    temp=sum-((k-prefix[i]%k)%k)+((k-(prefix[i]+1)%k)%k);
                    // pln(((char)(i+'a'))+" "+temp);
                    if(temp<=n-p-1){
                        idx=p;
                        chrr=(char)(i+'a');
                        break;
                    }
                }                
                sum=sum-((k-prefix[c-'a']%k)%k)+((k-((prefix[c-'a']+1)%k))%k);
                prefix[c-'a']++;
                p++;
            }
            // pln(chrr+" "+idx);
            StringBuilder sbr=new StringBuilder();
            for(int i=0;i<idx;i++)
                sbr.append(s.charAt(i));                
            sbr.append(chrr);
            // pln(sbr.toString());
            arr=new int [26];
            for(char c:sbr.toString().toCharArray()){
                arr[c-'a']++;
            }
            sum=0;
            for(int i=0;i<26;i++){
                arr[i]=(k-(arr[i]%k))%k;
                sum+=arr[i];
            }
            // pln(Arrays.toString(arr));
            arr[0]+=(n-idx-1)-sum;
            for(int i=0;i<26;i++){
                while(arr[i]-->0)
                    sbr.append((char)(i+'a'));
            }
            pln(sbr.toString());
        }
    }       
    public static int  findDiameter(int r, List<List<Integer>>list){
        return findFarthest(findFarthest(r,list)[0],list)[1];
    }
    public static int[] findFarthest(int u, List<List<Integer>>list){
        int n=list.size();
        boolean []vis=new boolean[n+1];
        Queue<Integer>q=new LinkedList<>();
        q.offer(u);
        vis[u]=true;
        int s,pr,cnt=0;
        int []ar=new int[]{u,0};
        while(q.size()>0){
            s=q.size();
            while(s-->0){
                pr=q.poll();
                if(ar[1]<cnt){
                    ar[1]=cnt;
                    ar[0]=pr;
                }
                for(int i:list.get(pr)){
                    if(!vis[i]){
                        vis[i]=true;
                        q.offer(i);
                    }
                }
            }
            cnt++;
        }
        return ar;
    }
    public static long atMostK(char []chrr, int k){
        if(k<0)
            return 0;
        int l=0,cnt=0;
        long ans=0l;
        for(int i=0;i<chrr.length;i++){
            if(chrr[i]=='1')
                cnt++;
            while(cnt>k){
                if(chrr[l++]=='1')
                    cnt--;
            }
            ans+=(long)(i-l)+1l;
        }
        return ans;
    }
    public static int ask(int l, int r){
        System.out.println("? "+l+" "+r);
        System.out.flush();
        return sc.nextInt();
    }
    public static void sort(long []arr){
        ArrayList<Long> list=new ArrayList<>();
        for(int i=0;i<arr.length;i++)
            list.add(arr[i]);
        Collections.sort(list);
        for(int i=0;i<arr.length;i++)
            arr[i]=list.get(i);
    }
    public static void swap(char []chrr, int i, int j){
        char temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static int countSetBits(long n){
        int a=0;
        while(n>0){
            a+=(n&1);
            n>>=1;
        }
        return a;
    }
    static class Pair{
        int v;
        String name;
        Pair(int a, String n){
            v=a;
            name=n;
        }
     //*
    }
    /*/
        public int compareTo(Pair p){
            return (b-p.b);
        }
        public int hashCode(){
            int hashcode = (a+" "+b).hashCode();
            return hashcode;
        }
        public boolean equals(Object obj){
            if (obj instanceof Pair) {
                Pair p = (Pair) obj;
                return (p.a==this.a && p.b == this.b);
            }
            return false;
        }
    }
    //*/
    static boolean isPrime(int n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        if (n % 2 == 0 || n % 3 == 0) 
            return false; 
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
                return false; 
        return true; 
    } 
    static long gcd(long a, long b) { 
        if (b == 0) 
            return a; 
        return a>b?gcd(b, a % b):gcd(a, b % a);  
    } 
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
    static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    public static int s(int n){
        return sc.nextInt();
    }
    public static long s(long n){
        return sc.nextLong();
    }
    public static String s(String n){
        return sc.next();
    }
    public static double s(double n){
        return sc.nextDouble();
    }
    public static void p(int n){
        pw.print(n);
    }
    public static void p(long n){
        pw.print(n);
    }
    public static void p(String n){
        pw.print(n);
    }
    public static void p(double n){
        pw.print(n);
    }
    public static void pln(int n){
        pw.println(n);
    }
    public static void pln(long n){
        pw.println(n);
    }
    public static void pln(String n){
        pw.println(n);
    }
    public static void pln(double n){
        pw.println(n);
    }
    public static void feedArr(long []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextLong();
    }
    public static void feedArr(double []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextDouble();
    }
    public static void feedArr(int []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextInt();
    }
    public static void feedArr(String []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.next();
    }
    public static String printArr(int []arr){
        StringBuilder sbr=new StringBuilder();
        for(int i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public  static String printArr(long []arr){
        StringBuilder sbr=new StringBuilder();
        for(long i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(String []arr){
        StringBuilder sbr=new StringBuilder();
        for(String i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(double []arr){
        StringBuilder sbr=new StringBuilder();
        for(double i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
//cbbbbbbbbccccccc