How to add a custom watermark for each pdf pages without creating a new one in memory using node.js

Question

I am working on project with pdf's, i want to add a custom watermark to each pages of pdf but only using 'input.pdf' and save it no 'output.pdf'.

I tried with pdf-lib.js but i can't achieve what i want

const fs = require('fs');
const {
    writeFileSync,
    readFileSync
} = require("fs");

async function createPDF() {
    const document = await PDFDocument.load(readFileSync("./f1.pdf-1675923413580.pdf"));

    const courierBoldFont = await document.embedFont(StandardFonts.Courier);
    const firstPage = document.getPage(0);

    const {
        width,
        height
    } = firstPage.getSize()
    firstPage.drawText('This text was added with JavaScript!', {
        x: 5,
        y: height / 2 + 300,
        size: 50,
        font: courierBoldFont ,
        color: rgb(0.95, 0.1, 0.1),
        rotate: degrees(-45),
    })

    writeFileSync("./output.pdf", await document.save());
}

createPDF().catch((err) => console.log(err));

Goal input.pdf + watermark = input.pdf done on itself