diff --git a/circom_circuits/Operations/generate_inputs_for_pol.py b/circom_circuits/Operations/generate_inputs_for_pol.py
index 53cf420..b1bf000 100755
--- a/circom_circuits/Operations/generate_inputs_for_pol.py
+++ b/circom_circuits/Operations/generate_inputs_for_pol.py
@@ -345,7 +345,7 @@ with open("input.json", "w") as file:
                 file.write('],')
             else:
                 file.write(',')
-        file.write('\n\t"unspent_root" :\t\t\t\t"'+str(cm_unspent_root)+'",')
+    file.write('\n\t"cm_unspent_root" :\t\t\t\t"'+str(cm_unspent_root)+'",')
     if anonymity == "private":
         file.write('\n\t"unspent_nodes" :\t\t\t\t\t[')
         for i in range(32):
@@ -365,7 +365,7 @@ with open("input.json", "w") as file:
                 file.write('],')
             else:
                 file.write(',')
-        file.write('\n\t"unspent_root" :\t\t\t\t"'+str(nf_root)+'",')
+    file.write('\n\t"nf_unspent_root" :\t\t\t\t"'+str(nf_root)+'",')
     file.write('\n\t"starting_slot" :\t\t\t\t"'+str(starting_slot)+'",')
     file.write('\n\t"secrets_root" :\t\t\t\t"'+str(secret_root)+'",')
     file.write('\n\t"state" :\t\t\t\t"'+str(state)+'",')
diff --git a/circom_circuits/Operations/pol.circom b/circom_circuits/Operations/pol.circom
index 7ff7e18..1e157ce 100644
--- a/circom_circuits/Operations/pol.circom
+++ b/circom_circuits/Operations/pol.circom
@@ -81,7 +81,8 @@ template proof_of_leadership(){
     signal input nf_next;
     signal input unspent_nodes[32];
     signal input unspent_selectors[32];         // must be bits
-    signal input unspent_root;                  // It's either the nullifier (if selector = 0) or the commitment root of the last state
+    signal input nf_unspent_root;
+    signal input cm_unspent_root;
 
     //Part of the secret key
     signal input starting_slot;
@@ -178,7 +179,7 @@ template proof_of_leadership(){
         unspent_membership.nodes[i] <== unspent_nodes[i];
         unspent_membership.selector[i] <== unspent_selectors[i];
     }
-    unspent_membership.root <== unspent_root;
+    unspent_membership.root <== (cm_unspent_root - nf_unspent_root) * selector + nf_unspent_root;
             //Compute the leaf if it's a private note representing previous nf pointing to next in the IMT
     component hash = Poseidon2_hash(2);
     hash.inp[0] <== nf_previous; 
@@ -226,4 +227,4 @@ template proof_of_leadership(){
     entropy_contrib <== entropy.out;
 } 
 
-component main {public [slot,epoch_nonce,t0,t1,commitments_aged_root,unspent_root,one_time_key]}= proof_of_leadership();
\ No newline at end of file
+component main {public [slot,epoch_nonce,t0,t1,commitments_aged_root,nf_unspent_root,cm_unspent_root,one_time_key]}= proof_of_leadership();
\ No newline at end of file