Create dynamic picklist in lwc

I have custom table with the multiple rows and there are two picklists in each row. Picklist options are as follows:

 @track picklist1 = [
      {value: 'w1', label: 'w1'},
      {value: 'w2', label: 'w2'}
    ];

    @track picklist2 = [
      {value: 'v1', label: 'v1'},
      {value: 'v2', label: 'v2'},
      {value: 'v3', label: 'v3'}
    ];

1. on select of w1 from picklist1, I want to load v1 and v2 in picklist2.
2. on select of w2 from picklist1, I want to load v2 and v3 in picklist2.

This should work for each row, i.e if 1st row picklist1 value is edited, then only 1st row picklist2 values should be updated and displayed.

html:

<td>
   <div>
      <div class="slds-select_container">
         <select class="slds-select" data-item={some id} onchange={handlePicklist1Change}>
            <option value="">Select</option>
            <template for:each ={picklist1} for:item="item">
               <option key={item.key} value={item.key}>{item.value}</option>
            </template>
         </select>
      </div>
   </div>
</td>
<td>
   <div>
      <div class="slds-select_container">
         <select class="slds-select" data-item={some id} onchange={handlePicklist2Change}>
            <option value="">Select</option>
            <template for:each ={picklist2} for:item="item">
               <option key={item.key} value={item.key}>{item.value}</option>
            </template>
         </select>
      </div>
   </div>
</td>

Js:

handlePicklist1Change(evt) {
    if (evt.target.value == "w1") {
        this.picklist2 = [{
                value: 'v1',
                label: 'v1'
            },
            {
                value: 'v2',
                label: 'v2'
            }
        ];
    }
    if (evt.target.value == "w2") {
        this.picklist2 = [{
                value: 'v2',
                label: 'v2'
            },
            {
                value: 'v3',
                label: 'v3'
            }
        ];
    }
}

I have tried above, but it updates all picklist2 in all rows.