Divisors [0]

Divisors [0]

Let's consider the string of all natural numbers: $1, 2, 3, 4, \ldots$

We'd like to find the sum of the first $n$ values of this sequence, although that alone is a bit boring (how would we do this?)

Instead, we'd like to find the sum, only after doing a simple operation to the individual sequence values - taking their value modulo some $m$.

For example, for $n=5$, $m=4$, the sequence of the first 5 elements would be: $1, 2, 3, 0, 1$, and the total sum would be 7.

Input

Input will contain two space-separated integers $n$ and $m$, mirroring the definition from the statement

Output

Output a single integer representing the sum of the first $n$ elements modulo $m$.

Constraints

• $1 \leq n \leq 10^9$
• $1 \leq m \leq 10^9$

Example

5 4

7