Segment Sum

题面翻译

给定 $l, r, k$，求 $[l, r]$ 之间的各数位上包含的不同数字不超过 $k$ 个的所有数的和。答案对 $998244353$ 取模。

保证 $1 \leq l \leq r \leq 10^{18}, 1 \leq k \leq 10$。

题目描述

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

输入格式

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.

输出格式

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

样例 #1

样例输入 #1

10 50 2

样例输出 #1

1230

样例 #2

样例输入 #2

1 2345 10

样例输出 #2

2750685

样例 #3

样例输入 #3

101 154 2

样例输出 #3

2189

提示

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 $ .