Alice is attempting to type a specific string on her computer. However, she tends to be clumsy and may press a key for too long, resulting in a character being typed multiple times.

You are given a string word, which represents the final output displayed on Alice's screen. You are also given a positive integer k.

Return the total number of possible original strings that Alice might have intended to type, if she was trying to type a string of size at least k.

Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Example 2:

Example 3:

Constraints:

• 1 <= word.length <= 5 * 105
• word consists only of lowercase English letters.
• 1 <= k <= 2000