Description

Last Sunday was a wonderful day! YC should have participated in the last contest which was determined on that day with JY and SB but it was such a pity that he has made some voice like "Gugugu" for absence. Something got worse because they needed one person who knew a little about "The Euler Sieves for Getting Primes" to solve the Signed problem in that occasion. However, SB was too young too simple and always so naive in the "Number-Theoretic" that JY had no choice but to solve that problem by himself and showed a picture.

In the Euler Sieves for Getting Primes, JY got a wrong set for primes due to missing a '=' in his code. In the other day, YC found the wrong set interesting so he selected all the composite number which in the wrong set to gained a new set "LYX". And then he came up with a new problem for you: He will give you an integer n and an integer m, you need to get all the number which are in the "LYX" and no less than n and no more than m then sorted them by size in ascending. Now you get a list "LYX"! Every number has its own index from 1 to k. Finally, he wants you to print :

（$\sum_{i=1}^k\sum_{j=1}^ka_i*a_j*[i+j==h]$）% 998244353 while h from 2*k to 2.

ATTENTION!!

If the value of $[i+j==h]$ is 1 when i+j==h, else is 0.

JY missed a '=' of the inner loop in the "Euler Sieves for Getting Primes" so that some numbers which had got were not used.

Format

Input

Mulity inputs, each line contains two integers n and m.

$1 \leq n,m \leq 1e12$，$22500 \leq m-n \leq 6e11$

Output

For each test case, output（$\sum_{i=1}^k\sum_{j=1}^ka_i*a_j*[i+j==h]$）% 998244353 while h from $2*k$ to $2$​.

Samples

50000 55000

950806815 702717133 359019419 413242813 658749135

Hints

Of course Sample 1 is not an right sample, because m-n should be larger than 22500.