Cats Dividing the Fish

Problem Description

There is a pile of fish on the beach, and $N$ little cats come to divide it. The first cat splits the pile into $N$ equal parts, leaving $i$ fish over ($i<N$); it throws those extra $i$ fish into the sea and takes away one part. The second cat then splits the remaining fish into $N$ equal parts, again leaving $i$ fish over, throws those $i$ fish into the sea, and takes away one part. The third, fourth, $\dots$, and $N$-th cats do the same: they split the final remaining fish into $N$ parts, throw away the extra $i$ fish, and take one part.

Write a program that reads the number of cats $N$ and the number $i$ of fish thrown into the sea each time, and outputs the minimum number of fish originally on the beach such that every cat can get its share.

For example, two cats divide the fish with $N=2$, throwing away $i=1$ fish each time. To let every cat eat, we can assume the second cat needs to take $1$ fish, so there are $3$ fish to be divided before its turn; then before the first cat's turn there were $3\times 2+1=7$ fish.

Input Format

A total of $2$ lines. The first line contains an integer $N$, the second line contains an integer $i$.

It is guaranteed that $0 < N < 10$ and $i < N$.

Output Format

One integer on a line, the minimum number of fish on the beach satisfying the requirement.

Sample Input

Sample Input 1

2
1

Sample Input 2

3
1

Sample Output

Sample Output 1

7

Sample Output 2

25

Sample Explanation

For sample 1, two cats divide the fish, throwing away $1$ fish each time. To let every cat eat, assume the second cat takes $1$ fish; then before its division there are $3$ fish remaining (split into $2$ parts with $1$ left over, throw away $1$, take $1$ part). When the first cat divides, it is also split into $2$ parts with $1$ left over, so the total number of fish is $3 \times 2 + 1 = 7$.

Constraints

• $0 < N < 10$
• $i < N$