B. Yet Another Meme Problem
math
You are given two integers \(A\) and \(B\), calculate the number of pairs \((a, b)\) such that \(1 \le a \le A\), \(1 \le b \le B\), and the equation \(a \cdot b + a + b = conc(a, b)\) is true; \(conc(a, b)\) is the concatenation of \(a\) and \(b\) (for example, \(conc(12, 23) = 1223\), \(conc(100, 11) = 10011\)). \(a\) and \(b\) should not contain leading zeroes.
The first line contains \(t\) (\(1 \le t \le 100\)) — the number of test cases.Each test case contains two integers \(A\) and \(B\) \((1 \le A, B \le 10^9)\).
Print one integer — the number of pairs \((a, b)\) such that \(1 \le a \le A\), \(1 \le b \le B\), and the equation \(a \cdot b + a + b = conc(a, b)\) is true.
There is only one suitable pair in the first test case: \(a = 1\), \(b = 9\) (\(1 + 9 + 1 \cdot 9 = 19\)).