34525번 - Balanced Integer 서브태스크다국어

문제

Since the CCO often uses integers, Alice needs to learn about the integers! A positive integer $n$ can be written in base $b$ as the sequence $d_{m−1}d_{m−2} \dots d_1d_0$ if the following hold:

• Each digit $d_i$ is between 0ドル$ and $b − 1,ドル inclusive.
• $d_{m−1} > 0$.
• $n = d_{m−1} \times b^{m−1} + d_{m−2} \times b^{m−2} + \cdots + d_1 \times b^1 + d_0 \times b^0$.

For example, the integer 2025ドル$ in base 19ドル$ is the sequence $(5, 11, 11)$ because 2025ドル = 5 \times 19^2 + 11 \times 19^1 + 11 \times 19^0$.

An integer $n$ is $b$-balanced if, when $n$ is written in base $b,ドル the average of the digits is $\frac{b − 1}{ 2}$.

For example, 2025ドル$ is 19ドル$-balanced because $\frac{5 + 11 + 11}{ 3} = 9 = \frac{19 − 1}{ 2}$.

Alice can easily find integers that are 19ドル$-balanced. However, she has trouble finding integers that are balanced in multiple ways. Given $B$ and $N,ドル please help Alice find the minimum integer $x$ such that:

• $x$ is $b$-balanced, for all 2ドル ≤ b ≤ B$.
• $x ≥ N$.

입력

The first line of input contains two space-separated integers $B$ and $N$ ($N ≥ 1$).

It is guaranteed that the answer does not exceed 10ドル^{18}$.

출력

Output the minimum integer $x$ from the problem statement.

제한

서브태스크

노트

Feel free to use these code snippets as part of your solution.

// Important: If x is 0, the result is undefined.
int base_2_length(unsigned long long x) {
 return 64-__builtin_clzll(x);
}
int base_2_sum(unsigned long long x) {
 return __builtin_popcountll(x);
}