B. Spilling the Juice
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Trotles gave Keys and array with $$$n$$$ integers. However since Keys is very clumsy, he spilled juice over some values of the array. So now, for some of the values of array, Keys only knows a interval of values that it could be.

Given $$$q$$$ queries, where each query gives you a left and right endpoint of a range and a target sum, determine whether Keys can choose a value for each of the uncertain intervals such that the sum of the segment denoted by the left and right endpoints achieve the target sum.

Input

The first line contains $$$n$$$ and $$$q$$$, the length of the array and the number of queries respectively. $$$1 \le n, q \le 10^5$$$.

The next $$$n$$$ lines contain either:

a) $$$1$$$ $$$a$$$ indicating that Keys knows this value of the array and it is equal to $$$a$$$. $$$1 \le a \le 1000$$$

b) $$$2$$$ $$$l$$$ $$$r$$$ indicating that Keys doesn't know this value and it could be anywhere from $$$l$$$ to $$$r$$$ inclusive. $$$1 \le l, r \le 1000$$$

The next $$$q$$$ lines contain 3 space separated numbers, $$$l$$$ $$$r$$$ $$$x$$$, the left endpoint, right endpoint, and target sum respectively. $$$1 \le l, r \le n$$$, $$$1 \le x \le 1000$$$

Output

The output contains $$$q$$$ lines. Each line should contain "yes" if it is possible to choose values of the intervals to reach the target sum or "no" if it is not (without the quotes). It is case insensitive.

Example
Input
10 8
2 4 266
2 5 401
1 202
2 4 101
2 3 179
2 6 210
2 3 373
1 312
2 8 463
1 447
5 9 374
1 4 139
3 6 160
3 5 81
9 10 433
6 6 367
2 10 270
2 3 197
Output
yes
no
no
no
no
no
no
no