{"raw_statement":[{"iden":"problem statement","content":"We have a sequence of $N$ integers: $A_1, A_2, \\cdots, A_N$.\nYou can perform the following operation between $0$ and $K$ times (inclusive):\n\n*   Choose two integers $i$ and $j$ such that $i \\neq j$, each between $1$ and $N$ (inclusive). Add $1$ to $A_i$ and $-1$ to $A_j$, possibly producing a negative element.\n\nCompute the maximum possible positive integer that divides every element of $A$ after the operations. Here a positive integer $x$ divides an integer $y$ if and only if there exists an integer $z$ such that $y = xz$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 500$\n*   $1 \\leq A_i \\leq 10^6$\n*   $0 \\leq K \\leq 10^9$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\cdots$ $A_{N-1}$ $A_{N}$"},{"iden":"sample input 1","content":"2 3\n8 20"},{"iden":"sample output 1","content":"7\n\n$7$ will divide every element of $A$ if, for example, we perform the following operation:\n\n*   Choose $i = 2, j = 1$. $A$ becomes $(7, 21)$.\n\nWe cannot reach the situation where $8$ or greater integer divides every element of $A$."},{"iden":"sample input 2","content":"2 10\n3 5"},{"iden":"sample output 2","content":"8\n\nConsider performing the following five operations:\n\n*   Choose $i = 2, j = 1$. $A$ becomes $(2, 6)$.\n*   Choose $i = 2, j = 1$. $A$ becomes $(1, 7)$.\n*   Choose $i = 2, j = 1$. $A$ becomes $(0, 8)$.\n*   Choose $i = 2, j = 1$. $A$ becomes $(-1, 9)$.\n*   Choose $i = 1, j = 2$. $A$ becomes $(0, 8)$.\n\nThen, $0 = 8 \\times 0$ and $8 = 8 \\times 1$, so $8$ divides every element of $A$. We cannot reach the situation where $9$ or greater integer divides every element of $A$."},{"iden":"sample input 3","content":"4 5\n10 1 2 22"},{"iden":"sample output 3","content":"7"},{"iden":"sample input 4","content":"8 7\n1 7 5 6 8 2 6 5"},{"iden":"sample output 4","content":"5"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}