Problem Description

Takahashi wants 2 trillion yen ($=2 \times 10^{12}$ yen). Takahashi's current savings are $A$ yen. If Takahashi has $t$ yen on a certain day, the next day his savings will increase by $1 + Kt$ yen.

In how many days will Takahashi's savings first exceed 2 trillion yen?

Input Format

The input is given from the standard input in the following format:

$ A $ $ K $

Output Format

Output the number of days it takes for Takahashi's savings to first exceed 2 trillion yen.

Sample Input and Output

Sample Input #1

1000 300

Sample Output #1

4

Sample Input #2

6 2

Sample Output #2

25

Sample Input #3

567876543 0

Sample Output #3

1999432123457

Notes/Hints

Constraints

• $0 \leq A$
• $0 \leq K \leq 10^6$
• All inputs are integers

见题面 Input 部分

见题面 Output 部分