B"Dreamoon saw a large integer x written on the ground and wants to print its binary form out. Dreamoon has accomplished the part of turning x into its binary format. Now he is going to print it in the following manner. He has an integer n xe2 x80 x89= xe2 x80 x890 and can only perform the following two operations in any order for unlimited times each: Let's define an ideal sequence as a sequence of operations that can successfully print binary representation of x without leading zeros and ends with a print operation (i.e. operation 1). Dreamoon wants to know how many different ideal sequences are there and the length (in operations) of the shortest ideal sequence. The answers might be large so please print them modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). Let's define the string representation of an ideal sequence as a string of '1' and '2' where the i-th character in the string matches the i-th operation performed. Two ideal sequences are called different if their string representations are different. The single line of the input contains a binary integer representing x (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89x xe2 x80 x89< xe2 x80 x8925000) without leading zeros. The first line of the output should contain an integer representing the number of different ideal sequences modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). The second line of the output contains an integer representing the minimal length of an ideal sequence modulo 1000000007 (109 xe2 x80 x89+ xe2 x80 x897). For the first sample, the shortest and the only ideal sequence is xc2 xab222221 xc2 xbb of length 6. For the second sample, there are three ideal sequences xc2 xab21211 xc2 xbb, xc2 xab212222222221 xc2 xbb, xc2 xab222222222222222222222222221 xc2 xbb. Among them the shortest one has length 5."...