CF831C Jury Marks

Polycarp watched TV-show where $ k $ jury members one by one rated a participant by adding him a certain number of points (may be negative, i. e. points were subtracted). Initially the participant had some score, and each the marks were one by one added to his score. It is known that the $ i $ -th jury member gave $ a_{i} $ points. Polycarp does not remember how many points the participant had before this $ k $ marks were given, but he remembers that among the scores announced after each of the $ k $ judges rated the participant there were $ n $ ( $ n

The first line contains two integers $ k $ and $ n $ ( $ 1

Print the number of options for the score the participant could have before the judges rated the participant. If Polycarp messes something up and there is no options, print "0" (without quotes).

The answer for the first example is $ 3 $ because initially the participant could have $ -10 $ , $ 10 $ or $ 15 $ points. In the second example there is only one correct initial score equaling to $ 4002000 $ .