The kid who learned to count#4483

The kid who learned to count

1 second
128 megabytes
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A kid goat works as a controller on a ferry. His task is to ensure that the ferry does not sink from excessive weight. Today, only two tickets remain for the boat, and the ferry can carry at most additional kilograms.

In this forest, there is a single long road along which the animals live. Help the kid goat determine whether he can find two passengers within a specified segment of the forest.

Input

The first line contains two numbers (2 \le n \le 10^6) and (1 \le k \le 10^9) — the number of animals in the forest and the remaining capacity of the ferry, respectively.

The second line contains integers — the mass of each animal.

Then follows a number (1 \le m \le 10^5) — the number of queries.

Each of the next lines contains three integers , , and :

  • If t = 1, then 1 \le l < r \le n. This means: check whether it is possible to choose two animals among those in the segment [l, r] so that their total mass does not exceed .

  • If t = 2, then 1 \le l \le n, 1 \le r \le 10^9. This means: update the mass of the animal with number to kilograms.

Output

For each query of type , print a line "Yes" if the kid goat can find two such passengers in the specified segment, and "No" otherwise.

Each query of type means that the mass of the animal with number is changed to kilograms.

Examples

Example 1

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