You're given a K-ary infinite tree rooted at a vertex numbered 1. All its edges are weighted 1 initially.

Any node $$X$$ will have exactly $$K$$ children numbered as:

$$[ K*X + 0, K*X + 1, K*X + 2, K*X + 3, K*X + 4,....... K*X + (K - 1) ]$$

You are given $$Q$$ queries to answer which will be of the following two types:

$$1 u v$$: Print the shortest distance between nodes $$u$$ and $$v$$.
$$2 u v w$$: Increase the weight of all edges on the shortest path between $$u$$ and $$v$$ by $$w$$.

Input format

The first line contains two space-separated integers $$K$$ and $$Q$$.
Next $$Q$$ lines contain queries which will be of 2 types:
- Three space-separated integers $$1$$, $$u$$, and $$v$$
- Four space-separated integers $$2$$, $$u$$, $$v$$, and $$w$$

Output format

For each query of type $$(1 u v)$$, print a single integer denoting the shortest distance between $$u$$ and $$v$$.

Constraints

\(2 ≤ K ≤ 10\\ 1 ≤ Q ≤ 10^3\\ 1 ≤ U, V ≤ 10^{18}\\ U ≠ V\\ 1 ≤ W ≤ 10^9\)