Investments

Sashko has a bank account with an initial balance of $100$ hryvnias.

The bank annually credits an interest of $1\%$ based on the scheme of compound interest. However, the bank does not deal with kopecks: after each interest application, the fractional part is simply discarded — without rounding.

For example:

- after the first year, there will be $101$ hryvnias ($1\%$ of $100$ is $1$);

- after the second year, there will be $102$ hryvnias ($1\%$ of $101$ $\approx 1.01$, discard the kopecks);

- after the third year, there will be $103$ hryvnias ($1\%$ of $102$ $\approx 1.02$, again without kopecks).

Sashko neither deposits nor withdraws money from the account. It is necessary to determine how many years it will take for his balance to first reach or exceed $X$ hryvnias.