Arthur is a spy from the renowned secret agency MI-9548. In his missions, for security reasons, he uses the most sophisticated encryption algorithm to communicate with headquarters: the Shift Cipher.

The messages sent by Arthur are represented by lists containing integer values between $$$0$$$ and $$$9999$$$. The Shift Cipher consists of choosing a "shift" between $$$0$$$ and $$$9999$$$ and adding that same value to all elements of the list. If this application causes the value of an element to exceed $$$9999$$$, the remainder of the value when divided by $$$10000$$$ should be taken.

For example, if Arthur's message is $$$[1, 2, 3, 4]$$$ and we choose the shift $$$3$$$, we will have the new list $$$[4, 5, 6, 7]$$$. If we choose the shift $$$9998$$$, we will have the list $$$[9999, 0, 1, 2]$$$.

Arthur has a favorite phrase $$$B$$$, represented by a list of numbers, and he would like to choose the encryption shift in such a way that this phrase appears as many times as possible in the encrypted message.

For example, if the message to be encrypted is $$$[1, 2, 3, 1, 2]$$$ and Arthur likes the phrase $$$[6, 7]$$$, he should choose the shift $$$5$$$, as this will result in the message $$$[6, 7, 8, 6, 7]$$$, which contains Arthur's phrase twice.

Help Arthur by finding the shift that results in the highest number of occurrences of his favorite phrase in the message $$$A$$$ to be encrypted, and additionally report the number of occurrences. If more than one shift maximizes the number of occurrences, find the smallest one.