2913: Recursive sequence

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 i⁴. 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 < 2³¹ 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.

2
3 1 2
4 1 10

85
369

In the first case, the third number is 85 = 2∗1+2+3⁴. In the second case, the third number is 93 = 2∗1+1∗10+3⁴ and the fourth number is 369 = 2 ∗ 10 + 93 + 4⁴.