407475: GYM102801 C Function

Define function $$$f(x)= \prod \limits_{i=1}^{len} (x\%10^i)\%(x+1)$$$, where $$$len$$$ represents the digit length of $$$x$$$.

For example, $$$f(1023)=(3*23*23*1023)\%1024$$$.

Define function $$$g(n,m)= \begin{cases} f(g(n,m-1))& {m>1}\\ f(n)& {m=1} \end{cases}$$$. For example, $$$g(n,2)=f(f(n))$$$.

You are given $$$n$$$ and $$$m$$$, please calculate $$$\sum\limits_{i=1}^m g(n,i)$$$.

The input consists of multiple test cases.

The first line contains an integer $$$T$$$ $$$(1 \leq T \leq 20)$$$ — the number of test cases. The description of the test cases follows.

The only line contains two integers $$$n,m$$$ $$$(1 \leq n,m \leq 10^9)$$$ .

For each test case, print the answer.

2
3 4
4102 642

12
21262