P6788 "EZEC-3" April Sakura

$$Once again it is a spring day when sakura dance in the air,$$ $$Buds, like countless stars, sparkle on the branches and play with spring,$$ $$Hearts understand each other;$$ $$It is also the season of “flower snow” blown by the wind,$$ $$Stamens draw thousands of bees and butterflies to the treetops to whisper with spring,$$ $$Hearts hold their thoughts.$$ $$They bloom, suddenly in a single night,$$ $$Sakura like flaming trees gather and blossom across mountains and fields, like a vast sea;$$ $$Sakura on the earth,$$ $$Pleasing to the eye, they bloom and dye the forests, like clouds of rosy霞;$$ $$Even with three thousand worries,$$ $$Under the bright sunshine, one can let go and smile gently;$$ $$Even with endless gloom,$$ $$It is better to end it lightly in the warm breeze.$$ [—— "April Sakura"](http://music.163.com/song?id=1355079681&userid=587823498) 

In April, when sakura are in full bloom, ```Muxii``` looked at the sakura falling all over the sky and asked ```ZZH``` beside him: "Exactly how many sakura petals fall in this April?" ```ZZH``` answered: "The number of fallen sakura, $s$, and time $t$ satisfy the following relation: $$s=\prod_{x=1}^t\prod_{y|x}\frac{y^{d(y)}}{\prod_{z|y}(z+1)^2}$$ where $d(y)$ denotes the number of divisors of $y$." But as a ~~liberal arts student~~ beginner, ```Muxii``` obviously could not clearly know the exact value, so he had to keep asking ```ZZH``` for the answer to this question. Since the value may be very large, you only need to tell ```Muxii``` the result of the answer modulo $p$ for ```ZZH```.

Two positive integers $t$ and $p$, representing the time asked by ```Muxii``` and the modulus, respectively.

Output a positive integer $s$, representing the number of fallen sakura. Output the answer modulo $p$.

**"Sample 1 Explanation"** By direct substitution, the answer is $\frac1{2073600}$. Since the modular inverse of $2073600$ modulo $998244353$ is $648735108$, the final answer is $1×648735108\bmod998244353 = 648735108$. **"Constraints and Notes"** **The testdata guarantees that in the fraction in lowest terms of the answer, the denominator does not contain $p$ or any multiple of $p$.** For all testdata, it is guaranteed that $1\leq t\leq 2.5×10^9$, $9.9×10^8