Two Snuke

Given is an integer N. Snuke will choose integers s_1, s_2, n_1, n_2, u_1, u_2, k_1, k_2, e_1, and e_2 so that all of the following six conditions will be satisfied:

• 0 \leq s_1 < s_2
• 0 \leq n_1 < n_2
• 0 \leq u_1 < u_2
• 0 \leq k_1 < k_2
• 0 \leq e_1 < e_2
• s_1 + s_2 + n_1 + n_2 + u_1 + u_2 + k_1 + k_2 + e_1 + e_2 \leq N

For every possible choice (s_1,s_2,n_1,n_2,u_1,u_2,k_1,k_2,e_1,e_2), compute (s_2 − s_1)(n_2 − n_1)(u_2 − u_1)(k_2 - k_1)(e_2 - e_1), and find the sum of all computed values, modulo (10^{9} +7).

Solve this problem for each of the T test cases given.

Constraints

• All values in input are integers.
• 1 \leq T \leq 100
• 1 \leq N \leq 10^{9}

Input

Input is given from Standard Input in the following format:

T \mathrm{case}_1 \vdots \mathrm{case}_T

Each case is given in the following format:

N

Output

Print T lines. The i-th line should contain the answer to the i-th test case.

Example

Input

4 4 6 10 1000000000

Output

0 11 4598 257255556

inputFormat

input are integers.

• 1 \leq T \leq 100
• 1 \leq N \leq 10^{9}

Input

Input is given from Standard Input in the following format:

T \mathrm{case}_1 \vdots \mathrm{case}_T

Each case is given in the following format:

N

outputFormat

Output

Print T lines. The i-th line should contain the answer to the i-th test case.

Example

Input

4 4 6 10 1000000000

Output

0 11 4598 257255556

样例

4
4
6
10
1000000000

0
11
4598
257255556

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