public static int maxLength(String X, String Y, int K) {
        int n = X.length();
        int cost = 0, len = 0, maxlen = 0;
        for (int i = 0; i < n; i++) {
            cost += Math.abs(X.charAt(i) - Y.charAt(i)); // calculate the cost of changing the characters at each index i within the window.
            len++;
            while (cost > K) { // if the total cost of changing the characters within the window is more than K, shrink the window from the left to decrease the cost.
                cost -= Math.abs(X.charAt(i - len + 1) - Y.charAt(i - len + 1));
                len--;
            }
            maxlen = Math.max(maxlen, len); // update the maximum length seen so far.
        }
        return maxlen;
    }