Vitya loves programming and problem solving, but sometimes, to distract himself a little, he plays computer games. Once he found a new interesting game about tanks, and he liked it so much that he went through almost all levels in one day. Remained only the last level, which was too tricky. Then Vitya remembered that he is a programmer, and wrote a program that helped him to pass this difficult level. Try do the same. The game is organized as follows. There is a long road, two cells wide and n cells long. Some cells have obstacles. You control a tank that occupies one cell. Initially, the tank is located before the start of the road, in a cell with coordinates (0, 1) . Your task is to move the tank to the end of the road, to the cell ( n + 1, 1) or ( n + 1, 2) . Every second the tank moves one cell to the right: the coordinate x is increased by one. When you press the up or down arrow keys, the tank instantly changes the lane, that is, the y coordinate. When you press the spacebar, the tank shoots, and the nearest obstacle along the lane in which the tank rides is instantly destroyed. In order to load a gun, the tank needs t seconds. Initially, the gun is not loaded, that means, the first shot can be made only after t seconds after the tank starts to move. If at some point the tank is in the same cell with an obstacle not yet destroyed, it burns out. If you press the arrow exactly at the moment when the tank moves forward, the tank will first move forward, and then change the lane, so it will not be possible to move diagonally. Your task is to find out whether it is possible to pass the level, and if possible, to find the order of actions the player need to make. The first line contains four integers n , m 1 , m 2 and t , the length of the field, the number of obstacles in the first lane, the number of obstacles in the second lane and the number of tank steps before reloading, respectively ( 1 ≤ n ≤ 10 9 ; 0 ≤ m 1 , m 2 ≤ n ; 0 ≤ m 1 + m 2 ≤ 10 6 ; 1 ≤ t ≤