{"raw_statement":[{"iden":"problem statement","content":"There are $N$ kinds of materials. Material $i$ has a magic power of $A_i$.\nTakahashi, the magician, wants to make a potion by choosing one or more kinds from these materials and mixing them.\nAt the moment when he makes a potion by mixing $k$ kinds of materials, the magic power of the potion is the sum of the materials used. Then, every second, its magic power increases by $k$. Note that the increase of the magic power is a discrete - not continuous - process.\nTakahashi will mix materials just once, at time $0$. What is the earliest time he can get a potion with a magic power of exactly $X$?\nUnder the constraints, it can be proved that it is possible to make a potion with a magic power of exactly $X$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 100$\n*   $1 \\leq A_i \\leq 10^7$\n*   $10^9 \\leq X \\leq 10^{18}$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $X$\n$A_1$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"3 9999999999\n3 6 8"},{"iden":"sample output 1","content":"4999999994\n\nThe potion made by mixing Material $1$ and Material $3$ has a magic power of $3+8=11$ at time $0$, and it increases by $2$ every second, so it will be $9999999999$ at time $4999999994$, which is the earliest possible time.\nThe potion made by mixing all the materials $1, 2, 3$ will have a magic power of $9999999998$ at time $3333333327$ and $10000000001$ at time $3333333328$, so it will never be exactly $9999999999$."},{"iden":"sample input 2","content":"1 1000000000000000000\n1"},{"iden":"sample output 2","content":"999999999999999999"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}