Farmer John likes to play mathematics games with his N cows. Recently, they are attracted by recursive sequences. In each turn, the cows would stand in a line, while John writes two positive numbers a and b on a blackboard. And then, the cows would say their identity number one by one. The first cow says the first number a and the second says the second number b. After that, the i-th cow says the sum of twice the (i-2)-th number, the (i-1)-th number, and $ i^4$. Now, you need to write a program to calculate the number of the N-th cow in order to check if John’s cows can make it right.
The first line of input contains an integer t, the number of test cases. t test cases follow.
Each case contains only one line with three numbers N, a and b where N,a,b < $2^{31}$ as described above.
For each test case, output the number of the N-th cow. This number might be very large, so you need to output it modulo 2147493647.