A chip was placed on a field with coordinate system onto point (0, 0) . Every second the chip moves randomly. If the chip is currently at a point ( x , y ) , after a second it moves to the point ( x - 1, y ) with probability p 1 , to the point ( x , y - 1) with probability p 2 , to the point ( x + 1, y ) with probability p 3 and to the point ( x , y + 1) with probability p 4 . It's guaranteed that p 1 + p 2 + p 3 + p 4 = 1 . The moves are independent. Find out the expected time after which chip will move away from origin at a distance greater than R (i.e. will be satisfied). First line contains five integers R , a 1 , a 2 , a 3 and a 4 ( 0 ≤ R ≤ 50, 1 ≤ a 1 , a 2 , a 3 , a 4 ≤ 1000 ). Probabilities p i can be calculated using formula . It can be shown that answer for this problem is always a rational number of form , where . Print P · Q - 1 modulo 10 9 + 7 . In the first example initially the chip is located at a distance 0 from origin. In one second chip will move to distance 1 is some direction, so distance to origin will become 1 . Answers to the second and the third tests: and .