Farmer John's $N$ cows, conveniently numbered $1 \ldots N$, are all standing in a row (they seem to do so often that it now takes very little prompting from Farmer John to line them up). Each cow has a breed ID: 1 for Holsteins, 2 for Guernseys, and 3 for Jerseys. Farmer John would like your help counting the number of cows of each breed that lie within certain intervals of the ordering.

Input

The first line of input contains $N$ and $Q$ ($1 \leq N \leq 100,000$, $1 \leq Q \leq 100,000$).

The next $N$ lines contain an integer that is either 1, 2, or 3, giving the breed ID of a single cow in the ordering.

The next $Q$ lines describe a query in the form of two integers $a, b$ ($a \leq b$).

Output

For each of the $Q$ queries $(a,b)$, print a line containing three numbers: the number of cows numbered $a \ldots b$ that are Holsteins (breed 1), Guernseys (breed 2), and Jerseys (breed 3).

Examples

Input 1

6 3
2
1
1
3
2
1
1 6
3 3
2 4

Output 1

3 2 1
1 0 0
2 0 1

Problem credits: Nick Wu