You have an LED display capable of showing an $$$n$$$-digit integer, where each digit is represented using the standard $$$7$$$-segment layout.

Initially, each of the $$$7$$$ digit segments in every digit block may be in one of three states:

• Functional (denoted by 'W'): behaves correctly, i.e., it lights up or turns off as required by the digit being displayed;
• Stuck ON (denoted by '1'): always lit regardless of the digit being displayed;
• Stuck OFF (denoted by '0'): always unlit regardless of the digit being displayed.

You can renovate at most $$$k$$$ digit segments, i.e., convert at most $$$k$$$ digit segments into functional. You need to maximize the number of integers that can be correctly displayed and find the number of ways to achieve the maximum. Note that you can renovate digit segments that are initially functional, and each digit segment can be renovated at most once. Two ways of renovation are considered different if there is at least one digit segment that is renovated in one way but not in the other.

An integer is correctly displayed if and only if:

• It has no leading zeros, unless the integer is exactly $$$0$$$;
• It is right-aligned on the display: if the integer has $$$d$$$ ($$$1 \le d \le n$$$) digits, then only the rightmost $$$d$$$ digit blocks are used, and the leftmost $$$(n - d)$$$ blocks should be left blank and show nothing;
• For each of the $$$d$$$ used digit blocks, all $$$7$$$ digit segments match the target digit's display pattern when functional segments show the correct state for that digit and faulty segments remain stuck in their state.