There are piles of sand in a line. The th pile from the left initially has units of sand. Answer queries, the th query contains integers , , and :

If is `1`

: move units of sand from the th pile to the ()th pile. ().

If is `2`

: move units of sand from the th pile to the ()th pile. ().

If is `3`

: find the total units of sand in all of the piles between pile and , inclusive. ().

The queries will never make you remove more sand from a pile than it contains, or move a negative amount of sand.

#### Constraints

##### Subtask 1 [40%]

All queries will have = .

##### Subtask 2 [60%]

No additional constraints.

#### Input Specification

The first line contains space-separated integers, and .

The second line contains space-separated integers, the th integer representing the units of sand in the th pile.

The next lines each contain space-separated integers: , , and .

#### Output Specification

For each query with , output a line containing a single integer: the total units of sand in all of the piles between pile and , inclusive.

#### Sample Input

```
5 6
4 2 10 3 4
3 2 4
1 2 2
2 3 8
3 1 3
2 1 4
3 2 5
```

#### Sample Output

```
15
8
21
```

#### Explanation for Sample

The piles are initially .

After the nd query they are .

After the rd query they are .

After the th query they are .

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