A collector is restoring an antique cipher machine made of a row of rotating wheels, each engraved with the 26 lowercase letters arranged in a cycle so that rotating a wheel forward past 'z' wraps back to 'a'. Wheel i currently shows the letter s[i] and must end up showing the target letter t[i]. Restoration proceeds through a fixed sequence of numbered sessions 1, 2, ..., k. In session number j, the collector may pick at most one wheel that has never been touched in any earlier session and rotate it forward by exactly j notches (wrapping cyclically); a session may also be skipped entirely, and no wheel may ever be touched twice. Determine whether every wheel can be brought to its exact target letter by the end of session k.

Input format

Line 1: the string s (lowercase letters), the wheels' current letters. Line 2: the string t (lowercase letters, the same length as s), the wheels' target letters. Line 3: a single integer k, the number of numbered sessions available.

Output format

Print YES if every wheel can reach its target letter using at most k sessions under the stated rules, or NO otherwise.

Constraints

• 1 <= length of s = length of t <= 10^5
• s and t consist only of lowercase English letters.
• 0 <= k <= 10^9

ab
bd
3

YES

aa
bb
1

NO