Pradyumn recently studied a new topic called Random Numbers and Pseudo Random Numbers. He came across a fact that all the programming languages never creates perfectly random numbers. They follow a certain logic to create random numbers. That's why numbers generated are called Pseudo Random Numbers. Now, Pradyumn thought to make Pseudo Random Numbers himself. He created a following function

generateRandomNumbers(size) {
    range = 1000000007
    multiplierOne = 2017
    multiplierSecond = 2027
    lastNumber = 0
    secondLastNumber = 1
    maxNumberGeneratedTillNow = 0
    list[size] // list of generated numbers
    for(I = 1;I <= size; ++I) {
        newNumber = (lastNumber * multiplierOne + secondLastNumber * multiplierSecond + maxNumberGeneratedTillNow) % range + 1
        secondLastNumber = lastNumber
        lastNumber = newNumber 
        list.ADD(newNumber)
    }
return list

Pradyumn asked Anmol to test his logic. Anmol thought to check certain numbers that can be created by this number or not. Pradyumn is tired after creating the logic. Pradyumn needs your help to answer Anmol Queries.

INPUT CONSTRAINTS
\(1 \le size \le 10^6\)
\(1 \le q \le 10^5\)
\(1 \le q_i \le 1000000007\)

INPUT FORMAT
Two space separated integers size and Q , where size denotes the size of randomly generated numbers and Q denotes number of queries.
Q number of lines describing the query value on each line given by Anmol.

OUTPUT FORMAT
If number can be created from given values and function, output "YES" else "NO" without quotes