For problem statement at 0-999/800-899/800-809/803/problemE.txt this is a correct solution, but verifier at 0-999/800-899/800-809/803/verifierE.go ends with All tests passed can you fix the verifier? ```go
package main
import (
"bufio"
"fmt"
"os"
)
func main() {
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n, k int
// Read n and k
if _, err := fmt.Fscan(in, &n, &k); err != nil {
return
}
var s string
// Read the sequence string
fmt.Fscan(in, &s)
// dp[i][j] stores the move ('W', 'L', 'D') taken to reach the state at step i with balance derived from j.
// The balance (wins - losses) can range from -k to k.
// To use array indices, we offset the balance by k.
// Index j corresponds to balance = j - k.
// The range of j is 0 to 2*k.
// Dimensions: (n+1) x (2*k + 1).
dp := make([][]byte, n+1)
for i := range dp {
dp[i] = make([]byte, 2*k+1)
}
// Base case: At step 0, balance is 0. 0 maps to index k.
// We mark dp[0][k] with a non-zero value to indicate it's a reachable state.
// The value itself doesn't matter for the start state, using 1.
dp[0][k] = 1
for i := 0; i < n; i++ {
for j := 0; j <= 2*k; j++ {
// If state is not reachable, skip
if dp[i][j] == 0 {
continue
}
currentBal := j - k
char := s[i]
// Try 'W' (Win)
if char == 'W' || char == '?' {
nextBal := currentBal + 1
valid := false
if i == n-1 {
// Last game: must result in absolute difference k
if nextBal == k || nextBal == -k {
valid = true
}
} else {
// Intermediate game: absolute difference must be strictly less than k
if nextBal > -k && nextBal < k {
valid = true
}
}
if valid {
dp[i+1][nextBal+k] = 'W'
}
}
// Try 'L' (Loss)
if char == 'L' || char == '?' {
nextBal := currentBal - 1
valid := false
if i == n-1 {
if nextBal == k || nextBal == -k {
valid = true
}
} else {
if nextBal > -k && nextBal < k {
valid = true
}
}
if valid {
dp[i+1][nextBal+k] = 'L'
}
}
// Try 'D' (Draw)
if char == 'D' || char == '?' {
nextBal := currentBal
valid := false
if i == n-1 {
// Cannot end on 'D' because |currentBal| < k, so |nextBal| < k.
// Unless k=0, but constraint says k >= 1.
} else {
if nextBal > -k && nextBal < k {
valid = true
}
}
if valid {
dp[i+1][nextBal+k] = 'D'
}
}
}
}
// Determine if any valid end state was reached
endIndex := -1
if dp[n][0] != 0 { // Balance -k
endIndex = 0
} else if dp[n][2*k] != 0 { // Balance k
endIndex = 2 * k
}
if endIndex == -1 {
fmt.Fprintln(out, "NO")
} else {
// Reconstruct the sequence by backtracking
res := make([]byte, n)
currJ := endIndex
for i := n; i > 0; i-- {
move := dp[i][currJ]
res[i-1] = move
if move == 'W' {
currJ -= 1 // Previous balance was current - 1
} else if move == 'L' {
currJ += 1 // Previous balance was current + 1
}
// If 'D', previous balance was same as current
}
fmt.Fprintln(out, string(res))
}
}
```