## 「NewCode 2019-3」 E. Big Integer

For little pupils, a very large number usually means an integer with many many digits. Let's define a class of big integers which consists only of the digit one $(11 \cdots 1)$. The first few integers in this class are $1, 11, 111, 1111 \cdots$. Denote $A(n)$ as the $n$-th smallest integer in this class. To make it even larger, we consider integers in the form of $A(a^b)$
. Now, given a prime number $p$ , how many pairs $(i, j)$ are there such that 1 $\leq i \leq n,\ 1 \leq j \leq m,\ A(i^j) \equiv 0(mod \ p)$

## 「SDOI2010」 古代猪文

iPig在大肥猪学校图书馆中查阅资料，得知远古时期猪文文字总个数为N。当然，一种语言如果字数很多，字典也相应会很大。当时的猪王国国王考虑到如果修一本字典，规模有可能远远超过康熙字典，花费的猪力、物力将难以估量。故考虑再三没有进行这一项劳猪伤财之举。当然，猪王国的文字后来随着历史变迁逐渐进行了简化，去掉了一些不常用的字。