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E. Segment Sum
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$11 + 22 + 33 + 44 = 110$$$.

Input

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.

Output

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

Examples
Input
10 50 2
Output
1230
Input
1 2345 10
Output
2750685
Input
101 154 2
Output
2189
Note

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 $$$101 + 110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118 + 119 + 121 + 122 + 131 + 133 + 141 + 144 + 151 = 2189$$$.