diff --git a/plonky2/examples/factorial.rs b/plonky2/examples/factorial.rs
index c4de7f65..9f292372 100644
--- a/plonky2/examples/factorial.rs
+++ b/plonky2/examples/factorial.rs
@@ -1,6 +1,6 @@
 use anyhow::Result;
 use plonky2::field::types::Field;
-use plonky2::iop::witness::PartialWitness;
+use plonky2::iop::witness::{PartialWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::circuit_data::CircuitConfig;
 use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
@@ -12,20 +12,24 @@ fn main() -> Result<()> {
 
     let config = CircuitConfig::standard_recursion_config();
 
-    let pw = PartialWitness::new();
     let mut builder = CircuitBuilder::<F, D>::new(config);
 
-    let mut cur_target = builder.one();
+    let initial = builder.add_virtual_target();
+    let mut cur_target = initial;
     for i in 2..101 {
         let i_target = builder.constant(F::from_canonical_u32(i));
         cur_target = builder.mul(cur_target, i_target);
     }
+    builder.register_public_input(initial);
     builder.register_public_input(cur_target);
 
+    let mut pw = PartialWitness::new();
+    pw.set_target(initial, F::ONE);
+
     let data = builder.build::<C>();
     let proof = data.prove(pw)?;
 
-    println!("100 factorial (mod |F|) is: {}", proof.public_inputs[0]);
+    println!("100 factorial (mod |F|) is: {}", proof.public_inputs[1]);
 
     data.verify(proof)
 }
diff --git a/plonky2/examples/fibonacci.rs b/plonky2/examples/fibonacci.rs
index bd7e70a0..d7a47c02 100644
--- a/plonky2/examples/fibonacci.rs
+++ b/plonky2/examples/fibonacci.rs
@@ -1,5 +1,6 @@
 use anyhow::Result;
-use plonky2::iop::witness::PartialWitness;
+use plonky2::field::types::Field;
+use plonky2::iop::witness::{PartialWitness, Witness};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
 use plonky2::plonk::circuit_data::CircuitConfig;
 use plonky2::plonk::config::{GenericConfig, PoseidonGoldilocksConfig};
@@ -11,24 +12,31 @@ fn main() -> Result<()> {
 
     let config = CircuitConfig::standard_recursion_config();
 
-    let pw = PartialWitness::new();
     let mut builder = CircuitBuilder::<F, D>::new(config);
 
-    let mut prev_target = builder.zero();
-    let mut cur_target = builder.one();
+    let initial_a = builder.add_virtual_target();
+    let initial_b = builder.add_virtual_target();
+    let mut prev_target = initial_a;
+    let mut cur_target = initial_b;
     for _ in 0..99 {
         let temp = builder.add(prev_target, cur_target);
         prev_target = cur_target;
         cur_target = temp;
     }
+    builder.register_public_input(initial_a);
+    builder.register_public_input(initial_b);
     builder.register_public_input(cur_target);
 
+    let mut pw = PartialWitness::new();
+    pw.set_target(initial_a, F::ZERO);
+    pw.set_target(initial_b, F::ONE);
+
     let data = builder.build::<C>();
     let proof = data.prove(pw)?;
 
     println!(
         "100th Fibonacci number (mod |F|) is: {}",
-        proof.public_inputs[0]
+        proof.public_inputs[2]
     );
 
     data.verify(proof)