B"Frog Gorf is traveling through Swamp kingdom. Unfortunately, after a poor jump, he fell into a well of n meters depth. Now Gorf is on the bottom of the well and has a long way up. The surface of the well's walls vary in quality: somewhere they are slippery, but somewhere have convenient ledges. In other words, if Gorf is on x meters below ground level, then in one jump he can go up on any integer distance from 0 to a_x meters inclusive. (Note that Gorf can't jump down, only up). Unfortunately, Gorf has to take a break after each jump (including jump on 0 meters). And after jumping up to position x meters below ground level, he'll slip exactly b_x meters down while resting. Calculate the minimum number of jumps Gorf needs to reach ground level. The first line contains a single integer n ( 1 <= n <= 300 ,000 ) -- the depth of the well. The second line contains n integers a_1, a_2, ldots, a_n ( 0 <= a_i <= i ), where a_i is the maximum height Gorf can jump from i meters below ground level. The third line contains n integers b_1, b_2, ldots, b_n ( 0 <= b_i <= n - i ), where b_i is the distance Gorf will slip down if he takes a break on i meters below ground level. If Gorf can't reach ground level, print -1 . Otherwise, firstly print integer k -- the minimum possible number of jumps. Then print the sequence d_1, ,d_2, , ldots, ,d_k where d_j is the depth Gorf'll reach after the j -th jump, but before he'll slip down during the break. Ground level is equal to 0 . If there are multiple answers, print any of them. In the first example, Gorf is on the bottom of the well and jump to the height 1 meter below ground level. After that he slip down by meter and stays on height 2 meters below ground level. Now, from here, he can reach ground level in one jump. In the second example, Gorf can jump to one meter"...