Facebook Hacker Cup 2013 Round 1 Security Backtracking java solution too slow

Security.java

import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

/**
 * @author psy
 * 
 */
public class Security {

	private static final String IMPOSSIBLE = "IMPOSSIBLE";

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		List<String> output = new LinkedList<String>();

		Security testCase = new Security();

		int games = Integer.parseInt(in.nextLine());

		for (int i = 1; i <= games; i++) {
			String m = in.nextLine();
			String k1 = in.nextLine();
			String k2 = in.nextLine();

			String result = testCase.findKey(Integer.parseInt(m), k1, k2);

			output.add("Case #" + i + ": " + result);
		}

		for (String out : output) {
			System.out.println(out);
		}
	}

	public String findKey(int m, String k1, String k2) {

		int l = k1.length() / m;
		// split sections
		String regex = "(?<=\\G.{" + l + "})";
		List<String> k1Sections = Arrays.asList(k1.split(regex));
		List<String> k2Sections = Arrays.asList(k2.split(regex));

		return findKey(k1Sections, k2Sections);
	}

	private String findKey(List<String> k1Sections, List<String> k2Sections) {

		if (k1Sections.size() == 1) {
			if (matchSection(k1Sections.get(0), k2Sections.get(0))) {
				return lexSmall(k1Sections.get(0), k2Sections.get(0));
			} else {
				return IMPOSSIBLE;
			}
		}

		String s1 = k1Sections.get(0);

		String result = IMPOSSIBLE;

		for (String s2 : k2Sections) {

			if (matchSection(s1, s2)) {
				List<String> newK2Sections = new ArrayList<String>(k2Sections);
				newK2Sections.remove(s2);

				result = findKey(k1Sections.subList(1, k1Sections.size()), newK2Sections);
			}

			if (result != IMPOSSIBLE) {
				result = lexSmall(s1, s2) + result;
				break;
			}
		}

		return result;
	}

	private String lexSmall(String s1, String s2) {

		int length = s1.length();

		String result = "";

		for (int i = 0; i < length; i++) {

			char c1 = s1.charAt(i);
			char c2 = s2.charAt(i);

			if (c1 == '?') {
				if (c2 == '?') {
					result += 'a';
				} else {
					result += c2;
				}
			} else {
				result += c1;
			}
		}

		return result;
	}

	private boolean matchSection(String s1, String s2) {

		if (s1.equals(s2)) {
			return true;
		}

		// iterate
		int length = s1.length();
		for (int i = 0; i < length; i++) {

			if (s1.charAt(i) != '?' && s2.charAt(i) != '?' && s1.charAt(i) != s2.charAt(i)) {
				return false;
			}

		}

		return true;
	}

}