A12233. Segment Sum

You are given two integers $l$ and $r$ ( $l \le r$ ). Your task is to calculate the sum of numbers from $l$ to $r$ (including $l$ and $r$ ) such that each number contains at most $k$ different digits, and print this sum modulo $998244353$ .

For example, if $k = 1$ then you have to calculate all numbers from $l$ to $r$ such that each number is formed using only one digit. For $l = 10, r = 50$ the answer is $11 + 22 + 33 + 44 = 110$ .

The only line of the input contains three integers $l$ , $r$ and $k$ ( $1 \le l \le r < 10^{18}, 1 \le k \le 10$ ) — the borders of the segment and the maximum number of different digits.

Print one integer — the sum of numbers from $l$ to $r$ such that each number contains at most $k$ different digits, modulo $998244353$ .

For the first example the answer is just the sum of numbers from $l$ to $r$ which equals to $\frac{50 \cdot 51}{2} - \frac{9 \cdot 10}{2} = 1230$ . This example also explained in the problem statement but for $k = 1$ .

For the second example the answer is just the sum of numbers from $l$ to $r$ which equals to $\frac{2345 \cdot 2346}{2} = 2750685$ .

For the third example the answer is $101 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 121 + 122 + 131 + 133 + 141 + 144 + 151 = 2189$ .