Problem: Marina loves strings of the same length and Vasya loves when there is a third string, different from them in exactly t characters. Help Vasya find at least one such string.

More formally, you are given two strings s1, s2 of length n and number t. Let's denote as f(a, b) the number of characters in which strings a and b are different. Then your task will be to find any string s3 of length n, such that f(s1, s3) = f(s2, s3) = t. If there is no such string, print  - 1.

Input

The first line contains two integers n and t (1 ≤ n ≤ 105, 0 ≤ t ≤ n).

The second line contains string s1 of length n, consisting of lowercase English letters.

The third line contain string s2 of length n, consisting of lowercase English letters.

Output

Print a string of length n, differing from string s1 and from s2 in exactly t characters. Your string should consist only from lowercase English letters. If such string doesn't exist, print -1.

Examples

Input

3 2
abc
xyc


Output

ayd

Input

1 0
c
b


Output

-1

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class MainC {
	MyScanner sc = new MyScanner();
	Scanner sc2 = new Scanner(System.in);
	long start = System.currentTimeMillis();
	long fin = System.currentTimeMillis();
	final int MOD = 1000000007;
	int[] dx = { 1, 0, 0, -1 };
	int[] dy = { 0, 1, -1, 0 };

	void run() {
		int n = sc.nextInt();
		int t = sc.nextInt();

		char[] s1 = sc.next().toCharArray();
		char[] s2 = sc.next().toCharArray();
		int diff = 0;
		ArrayList<Integer> dPos = new ArrayList<Integer>();
		for (int i = 0; i < n; i++) {
			if (s1[i] != s2[i]) {
				diff++;
				dPos.add(i);
			}
		}

		StringBuilder out = new StringBuilder();
		if (t >= diff) {
			// 一致する箇所で変更しなければいけない文字の数
			int match = t - diff;
			for (int i = 0; i < n; i++) {
				if (s1[i] != s2[i]) {
					for (char c = 'a'; c <= 'z'; c++) {
						if (s1[i] != c && s2[i] != c) {
							out.append(c);
							break;
						}
					}
				} else {
					if (match > 0) {
						match--;
						for (char c = 'a'; c <= 'z'; c++) {
							if (s1[i] != c && s2[i] != c) {
								out.append(c);
								break;
							}
						}
					} else {
						out.append(s1[i]);
					}
				}
			}
		} else {
			// 一致させなければいけない個数
			int s1t = diff - t;
			int s2t = diff - t;
			for (int i = 0; i < n; i++) {
				if (s1[i] != s2[i]) {
					if (s1t > 0) {
						out.append(s1[i]);
						s1t--;
					} else if (s2t > 0) {
						out.append(s2[i]);
						s2t--;
					} else {
						for (char c = 'a'; c <= 'z'; c++) {
							if (s1[i] != c && s2[i] != c) {
								out.append(c);
								break;
							}
						}
					}
				} else {
					out.append(s1[i]);
				}
			}
			if (s1t > 0 || s2t > 0) {
				System.out.println(-1);
				return;
			}
		}
		System.out.println(out);
	}

	public static void main(String[] args) {
		new MainC().run();
	}

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	void debug2(int[][] array) {
		for (int i = 0; i < array.length; i++) {
			for (int j = 0; j < array[i].length; j++) {
				System.out.print(array[i][j]);
			}
			System.out.println();
		}
	}

	boolean inner(int h, int w, int limH, int limW) {
		return 0 <= h && h < limH && 0 <= w && w < limW;
	}

	void swap(int[] x, int a, int b) {
		int tmp = x[a];
		x[a] = x[b];
		x[b] = tmp;
	}

	// find minimum i (a[i] >= border)
	int lower_bound(int a[], int border) {
		int l = -1;
		int r = a.length;
		while (r - l > 1) {
			int mid = (l + r) / 2;
			if (border <= a[mid]) {
				r = mid;
			} else {
				l = mid;
			}
		}
		// r = l + 1
		return r;
	}

	boolean palindrome(String s) {
		for (int i = 0; i < s.length() / 2; i++) {
			if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
				return false;
			}
		}
		return true;
	}

	class MyScanner {
		int nextInt() {
			try {
				int c = System.in.read();
				while (c != '-' && (c < '0' || '9' < c))
					c = System.in.read();
				if (c == '-')
					return -nextInt();
				int res = 0;
				do {
					res *= 10;
					res += c - '0';
					c = System.in.read();
				} while ('0' <= c && c <= '9');
				return res;
			} catch (Exception e) {
				return -1;
			}
		}

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

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

		String next() {
			try {
				StringBuilder res = new StringBuilder("");
				int c = System.in.read();
				while (Character.isWhitespace(c))
					c = System.in.read();
				do {
					res.append((char) c);
				} while (!Character.isWhitespace(c = System.in.read()));
				return res.toString();
			} catch (Exception e) {
				return null;
			}
		}

		int[] nextIntArray(int n) {
			int[] in = new int[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextInt();
			}
			return in;
		}

		int[][] nextInt2dArray(int n, int m) {
			int[][] in = new int[n][m];
			for (int i = 0; i < n; i++) {
				in[i] = nextIntArray(m);
			}
			return in;
		}

		double[] nextDoubleArray(int n) {
			double[] in = new double[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextDouble();
			}
			return in;
		}

		long[] nextLongArray(int n) {
			long[] in = new long[n];
			for (int i = 0; i < n; i++) {
				in[i] = nextLong();
			}
			return in;
		}

		char[][] nextCharField(int n, int m) {
			char[][] in = new char[n][m];
			for (int i = 0; i < n; i++) {
				String s = sc.next();
				for (int j = 0; j < m; j++) {
					in[i][j] = s.charAt(j);
				}
			}
			return in;
		}
	}
}