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.util.*;
import java.io.*;
import java.math.*;

/**
 *
 * @Har_Har_Mahadev
 */

public class C {

	private static long INF = 2000000000000000000L, M = 1000000007, MM = 998244353;
	private static int N = 0;

	public static void process() throws IOException {

		int n = sc.nextInt(),k = sc.nextInt();
		String str = sc.next();
		if(n%k != 0) {
			System.out.println(-1);
			return;
		}
		int ans = search(str,n,k);
		if(ans == n) {
			System.out.println(str);
			return;
		}
		for(int e = str.charAt(ans)+1; e<='z'; e++) {
			StringBuilder res = new StringBuilder();
			int count[] = new int[300];
			for(int i = 0; i<ans; i++) {
				res.append(str.charAt(i));
				count[str.charAt(i)] = (count[str.charAt(i)] + k - 1)%k;
			}
			res.append((char)e);
			count[e] = (count[e] + k - 1)%k;
			int rem = 0;
			for(int i = 'a'; i<='z'; i++) {
				rem+=count[i];
			}
			
			if(rem+ans+1<=n) {
				int d = n-rem-ans-1;
				for(int i = 0; i<d; i++) {
					res.append('a');
				}
				for(int i = 'a'; i<='z'; i++) {
					while(count[i] != 0) {
						res.append((char)i);
						count[i]--;
					}
				}
				
				String val = res.toString();
				if(str.compareTo(val) <= 0) {
					System.out.println(val);
					return;
				}
				
			}
			
		}
		
	}

	private static int search(String str, int n, int k) {
		int l = 0,r = n;
		int ans = -1;
		while(l<=r) {
			int mid = (l+r)/2;
			StringBuilder res = new StringBuilder();
			int count[] = new int[300];
			for(int i = 0; i<mid; i++) {
				res.append(str.charAt(i));
				count[str.charAt(i)] = (count[str.charAt(i)] + k - 1)%k;
			}
			int rem = 0;
			for(int i = 'a'; i<='z'; i++) {
				rem+=count[i];
			}
			
			if(rem+mid<=n) {
				int d = n-rem-mid;
				for(int i = 0; i<d; i++) {
					res.append('z');
				}
				for(int i = 'z'; i>='a'; i--) {
					while(count[i] != 0) {
						res.append((char)i);
						count[i]--;
					}
				}
			}
			else {
				r = mid-1;
				continue;
			}
			String val = res.toString();
			if(str.compareTo(val) <= 0) {
				ans = mid;
				l = mid+1;
			}
			else {
				r = mid-1;
			}
		}
		return ans;
	}

	//=============================================================================
	//--------------------------The End---------------------------------
	//=============================================================================

	static FastScanner sc;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		boolean oj = true;
		if (oj) {
			sc = new FastScanner();
			out = new PrintWriter(System.out);
		} else {
			sc = new FastScanner(100);
			out = new PrintWriter("output.txt");
		}
		int t = 1;
		t = sc.nextInt();
		while (t-- > 0) {
			process();
		}
		out.flush();
		out.close();
	}

	static class Pair implements Comparable<Pair> {
		int x, y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			return Integer.compare(this.x, o.x);
		}

		//		 @Override
		//		    public boolean equals(Object o) {
		//		        if (this == o) return true;
		//		        if (!(o instanceof Pair)) return false;
		//		        Pair key = (Pair) o;
		//		        return x == key.x && y == key.y;
		//		    }
		//		 
		//		    @Override
		//		    public int hashCode() {
		//		        int result = x;
		//		        result = 31 * result + y;
		//		        return result;
		//		    }
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static void println(Object o) {
		out.println(o);
	}

	static void println() {
		out.println();
	}

	static void print(Object o) {
		out.print(o);
	}

	static void pflush(Object o) {
		out.println(o);
		out.flush();
	}

	static int ceil(int x, int y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static long ceil(long x, long y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static int max(int x, int y) {
		return Math.max(x, y);
	}

	static int min(int x, int y) {
		return Math.min(x, y);
	}

	static int abs(int x) {
		return Math.abs(x);
	}

	static long abs(long x) {
		return Math.abs(x);
	}

	static int log2(int N) {
		int result = (int) (Math.log(N) / Math.log(2));
		return result;
	}

	static long max(long x, long y) {
		return Math.max(x, y);
	}

	static long min(long x, long y) {
		return Math.min(x, y);
	}

	public static int gcd(int a, int b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.intValue();
	}

	public static long gcd(long a, long b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.longValue();
	}

	public static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int lcm(int a, int b) {
		return (a * b) / gcd(a, b);
	}

	public static int lower_bound(int[] arr, int x) {
		int low = 0, high = arr.length, mid = -1;

		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] >= x)
				high = mid;
			else
				low = mid + 1;
		}

		return low;
	}

	public static int upper_bound(int[] arr, int x) {
		int low = 0, high = arr.length, mid = -1;

		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] > x)
				high = mid;
			else
				low = mid + 1;
		}

		return low;
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() throws FileNotFoundException {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		FastScanner(int a) throws FileNotFoundException {
			br = new BufferedReader(new FileReader("input.txt"));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		String nextLine() throws IOException {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] readArray(int n) throws IOException {
			int[] A = new int[n];
			for (int i = 0; i != n; i++) {
				A[i] = sc.nextInt();
			}
			return A;
		}

		long[] readArrayLong(int n) throws IOException {
			long[] A = new long[n];
			for (int i = 0; i != n; i++) {
				A[i] = sc.nextLong();
			}
			return A;
		}
	}

	static void ruffleSort(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}

	static void ruffleSort(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}
}
