Tom and matrix

Time Limit: 3000/1500 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Tom was on the way home from school. He saw a matrix in the sky. He found that if we numbered rows and columns of the matrix from 0, then,
${a}_{i,j}=C_{i}^{j}$

if i < j, ${a}_{i,j}=0$

Tom suddenly had an idea. He wanted to know the sum of the numbers in some rectangles. Tom needed to go home quickly, so he wouldn't solve this problem by himself. Now he wants you to help him.
Because the number may be very large, output the answer to the problem modulo a prime p.

Input

Multi test cases(about 8). Each case occupies only one line, contains five integers, ${x}_{1}、{y}_{1}、{x}_{2}、{y}_{2}、p.
{x}_{1}\leq {x}_{2}\leq {10}^{5},{y}_{1}\leq {y}_{2}\leq {10}^{5},2\leq p\leq {10}^{9}$.

You should calculate $\sum_{i={x}_{1}}^{{x}_{2}}\sum_{j={y}_{1}}^{{y}_{2}}{a}_{i,j}$ mod p

Output

For each case, print one line, the answer to the problem modulo p.

Sample Input

0 0 1 1 7 1 1 2 2 13 1 0 2 1 2

Sample Output

3 4 1

Hint

hujie

Source

BestCoder Round #40

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