In Doodle Jump the aim is to guide a four-legged creature called "The Doodler" up a never-ending series of platforms without falling. — Wikipedia. It is a very popular game and xiaodao likes it very much. One day when playing the game she wondered whether there exists a platform that the doodler couldn't reach due to the limits of its jumping ability. Consider the following problem. There are n platforms. The height of the x -th ( 1 ≤ x ≤ n ) platform is a · x mod p , where a and p are positive co-prime integers. The maximum possible height of a Doodler's jump is h . That is, it can jump from height h 1 to height h 2 ( h 1 < h 2 ) if h 2 - h 1 ≤ h . Initially, the Doodler is on the ground, the height of which is 0. The question is whether it can reach the highest platform or not. For example, when a = 7 , n = 4 , p = 12 , h = 2 , the heights of the platforms are 7 , 2 , 9 , 4 as in the picture below. With the first jump the Doodler can jump to the platform at height 2 , with the second one the Doodler can jump to the platform at height 4 , but then it can't jump to any of the higher platforms. So, it can't reach the highest platform. User xiaodao thought about the problem for a long time but didn't solve it, so she asks you for help. Also, she has a lot of instances of the problem. Your task is solve all of these instances. The first line contains an integer t (1 ≤ t ≤ 10 4 ) — the number of problem instances. Each of the next t lines contains four integers a , n , p and h ( 1 ≤ a ≤ 10 9 , 1 ≤ n < p ≤ 10 9 , 0 ≤ h ≤ 10 9 ). It's guaranteed that a and p are co-prime. For each problem instance, if the Doodler can reach the highest platform, output " YES ", otherwise output " NO ".