In the first test case we have, $$a = 1, d = 3, K = 3, N = 3$$. Therefore, $$b_1 = 1, b_2 = 4, b_3 = 7$$. We need to sum over tuples of the form $$(v_1, v_2, v_3)$$ satisfying $$\sum\limits_{i=1}^{N} v_i = k$$.

For $$k = 0$$, we have only 1 tuple $$(0, 0, 0)$$, and the sum is $$1$$.
For $$k = 1$$, we have 3 possible tuples : $$(1, 0, 0), (0, 1, 0), (0, 0, 1)$$. The sum comes out to be $$b_1 + b_2 + b_3 = 1 + 4 + 7 = 12$$.
For $$k = 2$$, we have 6 possible tuples : $$(2, 0, 0), (0, 2, 0), (0, 0, 2), (1, 1, 0), (1, 0, 1), (0, 1, 1)$$. The sum comes out to be $$b_1^2 + b_2^2 + b_3^2 + b_1 * b_2 + b_2*b_3 + b_1 * b_3 = 1 + 16 + 49 + 4 + 28 + 7 = 105$$.
For $$k = 3$$, we have 10 possible tuples : $$(3, 0, 0), (0, 3, 0), (0, 0, 3), (1, 2, 0), (2, 1, 0), (0, 1, 2), $$$$(0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 1, 1)$$. The sum comes out to be $$b_1^3 + b_2^3 + b_3^3 + b_1 * b_2^2 + b_1^2 * b_2 + b_2 * b_3^2 + b_2 ^2 * b_3 + b_1 * b_3^2 + b_1^2 * b_3 + b_1 * b_2 * b_3 = 820$$.
Note that we output answers in a single line.

In the second test case we have, $$a = 2, d = 1, K = 2, N = 4$$. Therefore, $$b_1 = 2, b_2 = 3, b_3 = 4, b_4 = 5$$. We need to sum over tuples of the form $$(v_1, v_2, v_3, v_4)$$ satisfying $$\sum\limits_{i=1}^{N} v_i = k$$.

For $$k = 0$$, we have only 1 tuple $$(0, 0, 0)$$, and the sum is $$1$$.
For $$k = 1$$, we have 4 possible tuples : $$(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)$$. The sum comes out to be $$b_1 + b_2 + b_3 + b_4 = 2 + 3 + 4 + 5= 14$$.
For $$k = 2$$, we have 8 possible tuples. The sum comes out to be $$b_1^2 + b_2^2 + b_3^2 + b_4^2 + b_1 * b_2 + b_2*b_3 + b_1 * b_3 + b_1*b_4 + b_2*b_4 + b_3*b_4 = 125$$.
Note that we output answers in a single line.