John discovered a new game. To play this game you need a circle on which $$$k$$$ ($$$k$$$ can be any positive integer) numbers are placed. The player decides at which number he begins his game and is then forced to visit every number on the circle in clockwise order starting from his chosen position. At the beginning of the game, the player's health is $$$0$$$. When he visits a number, that number is added to his health. If at any point the player's health becomes negative, the game is lost.
To test John's understanding of the game, Ana gives him an array of $$$n$$$ integers and a series of $$$q$$$ queries. Each query consists of $$$2$$$ numbers $$$l$$$ and $$$r$$$ and corresponds to the following question: If the circle was filled with the numbers in the subsequence [$$$l$$$, $$$r$$$], would the game be winnable?
Help John answer the queries.
The first line contains two integers $$$n$$$ $$$(1 \le n \le 10^6)$$$ and $$$q$$$ $$$(1 \le q \le 10^6)$$$, the size of the array, and the number of queries.
The second line contains $$$n$$$ integers $$$a_i$$$ $$$( -10^9 \leq a_i \leq 10^9 )$$$, the given array.
Each of the next $$$q$$$ lines contains two integers $$$l$$$ and $$$r$$$ $$$(1 \le l \le r \le n)$$$, representing the given queries.
For each query, print "YES" if the game described by the query is winnable, or "NO" otherwise.
You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).
5 2 -4 3 5 -2 -10 2 4 4 5
YES NO
For the first query, we can pick $$$3$$$ as the starting point so we will visit the numbers in the following order: $$$3 \rightarrow 5 \rightarrow -2$$$. So our scores will be $$$3 \rightarrow 8 \rightarrow 6$$$.
For the second query, no matter the starting position the first number we will visit will be negative, thus instantly killing us.
