B"The only difference between easy and hard versions is on constraints. In this version constraints are higher. You can make hacks only if all versions of the problem are solved. Koa the Koala is at the beach! The beach consists (from left to right) of a shore, n+1 meters of sea and an island at n+1 meters from the shore. She measured the depth of the sea at 1, 2, ... , n meters from the shore and saved them in array d . d_i denotes the depth of the sea at i meters from the shore for 1 <= i <= n . Like any beach this one has tide, the intensity of the tide is measured by parameter k and affects all depths from the beginning at time t=0 in the following way: Formally, let's define 0 -indexed array p = [0, 1, 2, ldots, k - 2, k - 1, k, k - 1, k - 2, ldots, 2, 1] of length 2k . At time t ( 0 <= t ) depth at i meters from the shore equals d_i + p[t bmod 2k] ( t bmod 2k denotes the remainder of the division of t by 2k ). Note that the changes occur instantaneously after each second, see the notes for better understanding. At time t=0 Koa is standing at the shore and wants to get to the island. Suppose that at some time t ( 0 <= t ) she is at x ( 0 <= x <= n ) meters from the shore: Note that while Koa swims tide doesn't have effect on her (ie. she can't drown while swimming). Note that Koa can choose to stay on the shore for as long as she needs and neither the shore or the island are affected by the tide (they are solid ground and she won't drown there). Koa wants to know whether she can go from the shore to the island. Help her! The first line of the input contains one integer t ( 1 <= t <= 10^4 ) -- the number of test cases. Description of the test cases follows. The first line of each test case contains three integers n , k and l ( 1 <= n <= 3 cdot 10^5; 1 <= k <= 10^9; "...