For problem statement at 1000-1999/1500-1599/1550-1559/1558/problemB.txt this is a correct solution, but verifier at 1000-1999/1500-1599/1550-1559/1558/verifierB.go ends with All 100 tests passed can you fix the verifier? Looking at this problem, I need to find the number of ways to move a token from cell n to cell 1.
Let me define `dp[i]` = number of ways to reach cell 1 from cell i.
- `dp[1] = 1`
- For `i > 1`: `dp[i] = sum of dp[j]` for all j reachable from i in one move.
From cell x, I can reach:
1. Any cell `x - y` where `1 <= y <= x-1`, meaning cells `1` to `x-1` (subtraction)
2. Cell `floor(x/z)` for `z` from `2` to `x` (floored division)
So `dp[x] = (sum of dp[1..x-1]) + (sum of dp[floor(x/z)] for z=2..x)`
Let `S[x] = dp[1] + dp[2] + ... + dp[x]`
Then the subtraction part gives `S[x-1]`.
For the division part, I need `sum of dp[floor(x/z)] for z=2..x`.
The values `floor(x/z)` take O(sqrt(x)) distinct values. For each distinct value `v = floor(x/z)`, it appears for a range of z values. The count of z values giving the same floor is the number of times that value appears.
Let me think differently. Let `f[x]` = contribution from division moves from cell x = sum over z=2 to x of dp[floor(x/z)].
For each value v = floor(x/z), v ranges from 1 to floor(x/2). For a given v, the number of z in [2,x] with floor(x/z) = v is (number of z with floor(x/z)=v).
Actually, let me compute f[x] using the fact that floor(x/z) takes O(sqrt(x)) distinct values.
So `dp[x] = S[x-1] + f[x]` where `f[x] = sum_{z=2}^{x} dp[floor(x/z)]`.
Memory concern: n up to 4*10^6, and we need dp array and prefix sum array. Two arrays of int32 = 2 * 4MB * 4 = 32MB. Should be fine if limit is around 64MB.
Let me implement this:
```go
package main
import (
"bufio"
"fmt"
"os"
)
func main() {
reader := bufio.NewReader(os.Stdin)
writer := bufio.NewWriter(os.Stdout)
defer writer.Flush()
var n, m int
fmt.Fscan(reader, &n, &m)
dp := make([]int32, n+1)
S := make([]int32, n+1) // S[i] = dp[1]+...+dp[i]
dp[1] = 1
S[1] = 1
for x := 2; x <= n; x++ {
// subtraction part: S[x-1]
val := int64(S[x-1])
// division part: sum dp[floor(x/z)] for z=2..x
// floor(x/z) for z=2..x, values range from 1 to x/2
// enumerate distinct values using sqrt decomposition
z := 2
for z <= x {
q := x / z
// find max z' such that floor(x/z') = q
// z' = floor(x/q)
zMax := x / q
if zMax > x {
zMax = x
}
// count = zMax - z + 1
count := int64(zMax - z + 1)
val += count * int64(dp[q])
z = zMax + 1
}
dp[x] = int32(val % int64(m))
S[x] = int32((int64(S[x-1]) + int64(dp[x])) % int64(m))
}
fmt.Fprintln(writer, dp[n])
}
```
Let me verify with the example: n=3, m=some prime.
- dp[1]=1, S[1]=1
- x=2: subtraction: S[1]=1. Division: z=2, q=1, zMax=2, count=1, val+=1*dp[1]=1. val=2. dp[2]=2, S[2]=3.
- x=3: subtraction: S[2]=3. Division: z=2, q=1, zMax=3, count=2, val+=2*dp[1]=2. val=5. dp[3]=5. ✓
The answer matches the expected 5.