有没有办法在go中添加带有时间戳的io.multiwriter？

package main

import (
    "fmt"
    "io"
    "os"
    "time"
)

type TimestampWriter struct {
    writer io.Writer
}

func NewTimestampWriter(writer io.Writer) *TimestampWriter {
    return &TimestampWriter{writer: writer}
}

func (w *TimestampWriter) Write(p []byte) (n int, err error) {
    timestamp := time.Now().Format("2006-01-02 15:04:05")
    data := append([]byte(timestamp+" "), p...)
    return w.writer.Write(data)
}

func main() {
    file, err := os.Create("output.txt")
    if err != nil {
        fmt.Println("Failed to create file:", err)
        return
    }
    defer file.Close()

    timestampWriter := NewTimestampWriter(file)
    multiWriter := io.MultiWriter(timestampWriter, os.Stdout)

    fmt.Fprintln(multiWriter, "Hello, World!")
}